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If coefficients of the equation ax2 + bx + c = 0, a < 0 are real and roots of the equation are non–real complex and a + c + b < 0, then
- a)4a + c < 2b
- b)4a + c> 2b
- c)4a + c = 2b
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If coefficients of the equation ax2+ bx + c = 0, a <0 are real and ...
Method to Solve
Puting x=-1
a-b+c
but
a+c<b or a+c-b<0
hence f(x)<0 for all real values of x
therefore
putting x=-2
we get f(X)=4a+c-2b<0
or 4a+c<2b
a-b+c
but
a+c<b or a+c-b<0
hence f(x)<0 for all real values of x
therefore
putting x=-2
we get f(X)=4a+c-2b<0
or 4a+c<2b
Most Upvoted Answer
If coefficients of the equation ax2+ bx + c = 0, a <0 are real and ...
Given Information:
The given quadratic equation is ax^2 + bx + c = 0 where a < 0,="" the="" roots="" are="" non-real="" complex,="" and="" a="" +="" c="" +="" b="" />< />
To prove:
4a + c < />
Proof:
- Let the roots of the equation be α and β. Since the roots are non-real complex, they will be of the form α = p + qi and β = p - qi.
- Sum of roots, α + β = -b/a (By Vieta's formulas)
- Therefore, 2p = -b/a
- Since a < 0,="" we="" have="" a="-|a|." so,="" 2p="" />
- Also, product of roots, α * β = c/a (By Vieta's formulas)
- Therefore, (p^2 + q^2) = c/|a| and (p^2 + q^2) > 0
- Given a + c + b < 0,="" substituting="" the="" values,="" we="" get="" -|a|="" +="" c="" +="" b="" />< />
- Rearranging the terms gives 4a + c < />
Therefore, the correct option is A) 4a + c < 2b.="" />
The given quadratic equation is ax^2 + bx + c = 0 where a < 0,="" the="" roots="" are="" non-real="" complex,="" and="" a="" +="" c="" +="" b="" />< />
To prove:
4a + c < />
Proof:
- Let the roots of the equation be α and β. Since the roots are non-real complex, they will be of the form α = p + qi and β = p - qi.
- Sum of roots, α + β = -b/a (By Vieta's formulas)
- Therefore, 2p = -b/a
- Since a < 0,="" we="" have="" a="-|a|." so,="" 2p="" />
- Also, product of roots, α * β = c/a (By Vieta's formulas)
- Therefore, (p^2 + q^2) = c/|a| and (p^2 + q^2) > 0
- Given a + c + b < 0,="" substituting="" the="" values,="" we="" get="" -|a|="" +="" c="" +="" b="" />< />
- Rearranging the terms gives 4a + c < />
Therefore, the correct option is A) 4a + c < 2b.="" />
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If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer?
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If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If coefficients of the equation ax2+ bx + c = 0, a <0 are real and roots of the equation are non–real complex and a + c + b < 0, thena)4a + c < 2bb)4a + c> 2bc)4a + c = 2bd)none of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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