MCQ
Statement $A ($Assertion$)$ : If the roots are calculated by splitting the middle term, then $9 x^2-3 x-20=0\Rightarrow(3 x-5)(3 x+4)=0$
Statement $R ($Reason$)$: To factorise $a x^2+b x+c=0$, we write it in the form $a x^2+b_1 x+b_2 x+c=0$ such that $b_1+b_2=b$ and $b_1 b_2=a c$.
  • 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 $(A)$.
We have, $9 x^2-3 x-20=0$
$\Rightarrow 9 x^2-15 x+12 x-20=0 [$ By splitting the middle term $]$
$\Rightarrow 3 x(3 x-5)+4(3 x-5)=0$
$\Rightarrow(3 x+4)(3 x-5)=0$
$\therefore$ Both assertion and reason are true and reason is the correct explanation of assertion.

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