Statement A (Assertion) : A quadratic polynomial having 5 and -3 … - Vidyadip

MCQ

Statement A (Assertion) : A quadratic polynomial having 5 and -3 as zeroes is $x^2-2 x$ -15 .
Statement R (Reason): The quadratic polynomial having $\alpha$ and $\beta$ as zeroes is given by $p(x)=x^2-(\alpha+\beta) x+\alpha \beta$.

✓
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
C
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

Correct option: A.

Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.

(a) : Clearly, Reason is true.
Let $\alpha=5$ and $\beta=-3$.
Then, $\alpha+\beta=2$ and $\alpha \beta=-15$
$\therefore \quad$ Required polynomial is given by $p(x)=x^2-2 x-15$
$\therefore \quad$ Assertion and Reason both are true and Reason is the true explanation of Assertion.

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