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Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.
Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.
- a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
- b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
- c)Statement-1 is True, Statement-2 is False
- d)Statement-1 is False, Statement-2 is True
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Statement-1 : If a 4th degree polynomial function has four distinct re...
If a 4th degree polynomial function has four distinct real roots, then its graph will be like following
From graph we can say curve has 2 point of inflection.
Statement 1 is true
Statement 2 is not true.
From graph we can say curve has 2 point of inflection.
Statement 1 is true
Statement 2 is not true.
Most Upvoted Answer
Statement-1 : If a 4th degree polynomial function has four distinct re...
(x) = 0 has four distinct real roots, then the derivative function f'(x) has exactly two real roots.
Statement-1: This statement is not true. The number of inflection points of a polynomial function is determined by the degree of the polynomial. A 4th degree polynomial function can have 0, 1, or 2 inflection points. It is not necessary for a polynomial with four distinct real roots to have exactly two inflection points.
Statement-2: This statement is true. If a polynomial equation has four distinct real roots, then the derivative function will have at least three real roots, including the roots of the original polynomial. By the Intermediate Value Theorem, the derivative function must have at least one additional real root between each pair of consecutive roots of the original polynomial. Therefore, the derivative function will have at least two additional real roots, making a total of at least five real roots. However, it is also possible for the derivative function to have more than five real roots.
Statement-1: This statement is not true. The number of inflection points of a polynomial function is determined by the degree of the polynomial. A 4th degree polynomial function can have 0, 1, or 2 inflection points. It is not necessary for a polynomial with four distinct real roots to have exactly two inflection points.
Statement-2: This statement is true. If a polynomial equation has four distinct real roots, then the derivative function will have at least three real roots, including the roots of the original polynomial. By the Intermediate Value Theorem, the derivative function must have at least one additional real root between each pair of consecutive roots of the original polynomial. Therefore, the derivative function will have at least two additional real roots, making a total of at least five real roots. However, it is also possible for the derivative function to have more than five real roots.
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Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer?
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Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer?.
Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Statement-1 : If a 4th degree polynomial function has four distinct real roots, then its graph have exactly two inflection points.Statement-2 : If the equation f"(x) = 0 has distinct real roots, then the equation f(x) = 0 has atleast four real roots.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement-1 is True, Statement-2 is Falsed)Statement-1 is False, Statement-2 is TrueCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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