Statement A (Assertion) : 2 2 is a root of the quadratic equation… - Vidyadip

MCQ

Statement A (Assertion) : $2 \sqrt{2}$ is a root of the quadratic equation $x^2-4 \sqrt{2} x+8=0$.
Statement R (Reason) : The roots of a quadratic equation satisfy it.

✓
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.
Now, we have, $x^2-4 \sqrt{2} x+8=0$
$2 \sqrt{2}$ will be the root, if it will satisfy the given equation.
Now, $(2 \sqrt{2})^2-4 \sqrt{2}(2 \sqrt{2})+8=8-16+8=0$
Thus, $2 \sqrt{2}$ is a root of the given equation.
$\therefore \quad$ Both assertion and reason are true and reason is the correct explanation of assertion.

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