Question

Assertion :If $2,3$ are the zeroes of a quadratic polynomial, then polynomial is $x^2-5x+6.$ Reason: If $\alpha ,\beta$ are the zeroes of a monic quadratic polynomial, then polynomial is $x^2-(\alpha +\beta )x+\alpha \beta$.

• A. Both assertion and Reason are correct and reason is the correct explanation for Assertion
• B. Both assertion and reason are correct but reason is not the correct explanation for Assertion
• C. Assertion is correct but reason is incorrect
• D. Assertion is incorrect but reason is correct

Answer 1

The correct option is A Both assertion and Reason are correct and reason is the correct explanation for Assertion

Assertion
Let $f\left(x\right)=x^2-5x+6$
$f\left(x\right)=0\Rightarrow$ $x^2-5x+6=0$
$\Rightarrow (x-2)(x-3)=0$
$\Rightarrow x=2$ and $x=3$
$\therefore 2,3$ are the zeros of the polynomial $x^2-5x+6$
$\therefore$ Assertion is true.
Reason
Let $f\left(x\right)=x^2-(\alpha +\beta )x+\alpha \beta$
$f\left(x\right)=0\Rightarrow x^2-(\alpha +\beta )x+\alpha \beta =0$
$\Rightarrow (x-\alpha )(x-\beta )=0$
$\Rightarrow x=\alpha$ and $x=\beta$
$\therefore \alpha ,\beta$ are the zeroes of the polynomial $x^2-(\alpha +\beta )x+\alpha \beta$
$\therefore$ Reason is true
Since, both the Assertion and Reason are true and Reason is a correct explanation for Assertion.
The correct answer is A.