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If is α repeated root of the polynomial equation f(x) = 0, then
- a)f(a) = 0 but f'(a) ≠ 0
- b)f(a) ≠ 0 but f'(α) = 0
- c)f'(α) ≠ 0 and f'(α) = 0
- d)f(α) = 0 and f'(α) = 0
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If is α repeated root of the polynomial equation f(x) = 0, thena...
Since, α is the repeated root of the polynomial equation.
f(x) = 0, then f(a) = 0 and f'(α) = 0
Clearly , f(x) = sin x is continuous in the interval [0 ,π] and differentiable in the open interval [0 , π]
Also , f(0) = f(π) = 0, then by Rolle’s theorem
f '(c) = 0 => cos c = 0
c = π/2
f(x) = 0, then f(a) = 0 and f'(α) = 0
Clearly , f(x) = sin x is continuous in the interval [0 ,π] and differentiable in the open interval [0 , π]
Also , f(0) = f(π) = 0, then by Rolle’s theorem
f '(c) = 0 => cos c = 0
c = π/2
Most Upvoted Answer
If is α repeated root of the polynomial equation f(x) = 0, thena...
Since, α is the repeated root of the polynomial equation.
f(x) = 0, then f(a) = 0 and f'(α) = 0
Clearly , f(x) = sin x is continuous in the interval [0 ,π] and differentiable in the open interval [0 , π]
Also , f(0) = f(π) = 0, then by Rolle’s theorem
f '(c) = 0 => cos c = 0
c = π/2
f(x) = 0, then f(a) = 0 and f'(α) = 0
Clearly , f(x) = sin x is continuous in the interval [0 ,π] and differentiable in the open interval [0 , π]
Also , f(0) = f(π) = 0, then by Rolle’s theorem
f '(c) = 0 => cos c = 0
c = π/2
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If is α repeated root of the polynomial equation f(x) = 0, thena...
Repeating Root of a Polynomial Equation
An repeated root of a polynomial equation means that the root is a solution to the equation with a multiplicity greater than 1. In this case, if α is a repeated root of the polynomial equation f(x) = 0, it means that when you substitute α into the polynomial equation, it gives you 0.
Understanding the Options
a) f(α) = 0 but f(α) ≠ 0
This option is contradictory because if f(α) = 0, then f(α) cannot be not equal to 0.
b) f(α) ≠ 0 but f(α) = 0
This option is also contradictory because if f(α) = 0, then f(α) cannot be not equal to 0.
c) f(α) ≠ 0 and f(α) = 0
This option is contradictory because it states that f(α) is not equal to 0 and at the same time equal to 0.
Correct Answer: Option 'D'
d) f(α) = 0 and f(α) = 0
This option correctly states that when a root is repeated, it must satisfy the polynomial equation with a value of 0. Therefore, the correct answer is option 'D'.
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If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer?.
If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer?.
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If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If is α repeated root of the polynomial equation f(x) = 0, thena)f(a) = 0 but f'(a)≠ 0b)f(a)≠ 0 but f'(α) = 0c)f'(α) ≠0 and f'(α) = 0d)f(α) = 0 and f'(α) = 0Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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