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Properties of Conjugate of a Complex Number

Assertion :Th...

Question

Assertion :The equation $4 x^{3} - 9 x^{2} + 2 x + 1 = 0$ has atleast one real root in (0,1). Reason: If 'f' is a continuous function such that $\int_{a}^{b} f (x) = 0,$ the the equation f (x) = 0 has atleast one real root in (a,b).

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Reason is true (theory)
Assertion:
$f (x) = 4 x^{3} - 9 x^{2} + 2 x + 1 \Rightarrow \int_{0}^{1} f (x) d x = \int_{0}^{1} (4 x^{3} - 9 x^{2} + 2 x + 1) d x = {[\frac{4 x^{4}}{4} - \frac{9 x^{3}}{3} + \frac{2 x^{2}}{2} + x]}_{0}^{1} = 1 - 3 + 1 + 1 - 0 = 0$
Hence it is also true

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