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  • Please solve rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 1 maths textbook solution

Please solve rd sharma class 12 chapter 14 Mean Value Theoram exercise multiple choice question 1 maths textbook solution

Answers (1)

best_answer

Answer:

Option (c)

Hint:

You must know about the concept of roots of the equation.

Given:

Polynomial equation,

a_{n}x^{n}+a_{n-1\; }x^{n-1}+a_{n-2}\; x^{n-2}+....+a_{2}x^{2}+a_{1}x+a_{0}=0

n being a positive integer, has two different real roots \alpha and \beta .

Solution:

f(x)=a_{n}x^{n}+a_{n-1\; }x^{n-1}+a_{n-2}\; x^{n-2}+....+a_{2}x^{2}+a_{1}x+a_{0}=0

Now,   f(\alpha )=0                                [\because \alpha is root of equation]

          f(\beta )=0                                 [\because \beta is root of equation]

Now, f^{'}(x)=na_{n}x^{n-1}+(n-1)a_{n-1\; }x^{n-2}+....+a_{1}=0  has at least one root in \left [ \alpha ,\beta \right ] .

Hence, option (c) is correct.

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