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If the roots of the equation ax2 + bx + c = 0 are real and distinct, then
- a)both roots are greater than -b/2a
- b)both roots are less than -b/2a
- c)one of the roots exceeds -b/2a
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the roots of the equation ax2+ bx + c = 0 are real and distinct, th...
Solution:
Real and distinct roots of the given quadratic equation ax2 + bx + c = 0 are given by:
x = [-b ± √(b2 - 4ac)]/2a
Let us assume that the roots of the given equation are α and β, such that α < />
Therefore, α + β = -b/a < />
Also, α × β = c/a > 0
We know that the sum of roots of a quadratic equation is -b/a, and the product of roots is c/a.
Now, we need to find out whether one of the roots exceeds -b/2a.
Let us assume that α > -b/2a.
Then, β > -b/2a (because α < />
α + β > -b/a
2α > -b/a
2αa > -b
-4ac > -b2
b2 - 4ac < />
This contradicts the fact that the given quadratic equation has real and distinct roots.
Therefore, α cannot be greater than -b/2a.
Similarly, we can prove that β cannot be less than -b/2a.
Hence, the correct option is C, i.e., one of the roots exceeds -b/2a.
Real and distinct roots of the given quadratic equation ax2 + bx + c = 0 are given by:
x = [-b ± √(b2 - 4ac)]/2a
Let us assume that the roots of the given equation are α and β, such that α < />
Therefore, α + β = -b/a < />
Also, α × β = c/a > 0
We know that the sum of roots of a quadratic equation is -b/a, and the product of roots is c/a.
Now, we need to find out whether one of the roots exceeds -b/2a.
Let us assume that α > -b/2a.
Then, β > -b/2a (because α < />
α + β > -b/a
2α > -b/a
2αa > -b
-4ac > -b2
b2 - 4ac < />
This contradicts the fact that the given quadratic equation has real and distinct roots.
Therefore, α cannot be greater than -b/2a.
Similarly, we can prove that β cannot be less than -b/2a.
Hence, the correct option is C, i.e., one of the roots exceeds -b/2a.
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If the roots of the equation ax2+ bx + c = 0 are real and distinct, th...
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If the roots of the equation ax2+ bx + c = 0 are real and distinct, thena)both roots are greater than -b/2ab)both roots are less than-b/2ac)one of the roots exceeds-b/2ad)none of theseCorrect answer is option 'C'. Can you explain this answer?
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If the roots of the equation ax2+ bx + c = 0 are real and distinct, thena)both roots are greater than -b/2ab)both roots are less than-b/2ac)one of the roots exceeds-b/2ad)none of theseCorrect 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 If the roots of the equation ax2+ bx + c = 0 are real and distinct, thena)both roots are greater than -b/2ab)both roots are less than-b/2ac)one of the roots exceeds-b/2ad)none of theseCorrect 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 If the roots of the equation ax2+ bx + c = 0 are real and distinct, thena)both roots are greater than -b/2ab)both roots are less than-b/2ac)one of the roots exceeds-b/2ad)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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