Question

Assertion :If $f\left(x\right)$ is a quadratic expression such that $f\left(1\right)+f\left(2\right)=0$ . If $x=-1$ is root of $f\left(x\right)=0$, then other root is $\frac{8}{5}$ Reason: If $f\left(x\right)=a{x}^2+bx+c$ then $\alpha +\beta =-\frac{b}{a}$ & $\alpha \beta =\frac{c}{a}$

• 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. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

As $x=-1$ is root of $f\left(x\right)=0$

$\therefore f\left(x\right)=(x+1)(ax+b)$

Also $f\left(1\right)+f\left(2\right)=0$

$2(a+b)+3(2a+b)=0$

$\Rightarrow 8a+5b=0$

$\therefore -\frac{b}{a}=\frac{8}{5}$ = other root

Assertion $\left(A\right)$ and Reason $\left(R\right)$ both are correct but Reason $\left(R\right)$ is not proper explanation of Assertion $\left(A\right)$.