Assertion :Zeroes of $f (x) = x^{2} - 4 x - 5$ are 5,-1 Reason: The polynomial whose zeroes are $2 + \sqrt{2}, 2 - \sqrt{3}$ is $x^{2} - 4 x + 7$

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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Assertion is incorrect but Reason is correct

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Zeroes of $f (x) = x^{2} - 4 x - 5$ are obtained by solving:
$x^{2} - 4 x - 5 = 0$ , which implies
$x^{2} - 5 x + x - 5 = 0$
or, $x (x - 5) + 1 (x - 5) = 0$
which means $x = 5$ or $x = - 1$
Thus the assertion is correct.
However, the reason is incorrect. The numbers given are not the zeroes of $x^{2} - 4 x + 7$

Therefore, option $C$ is correct.

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Assertion :Zeroes of f(x)=x2−4x−5 are 5,-1 Reason: The polynomial whose zeroes are 2+√2,2−√3 is x2−4x+7

Assertion :Zeroes of $f (x) = x^{2} - 4 x - 5$ are 5,-1 Reason: The polynomial whose zeroes are $2 + \sqrt{2}, 2 - \sqrt{3}$ is $x^{2} - 4 x + 7$