Question

Assertion :If $\alpha ,\beta$ are the roots of equation $x^2+2(a-3)x+9=0$, $a\in R$ and $\alpha <6<\beta$, then $a<-\frac{3}{4}$. Reason: If $f\left(x\right)=x^2+2(a-3)x+9$, then $f\left(6\right)<0\Rightarrow a<-\frac{3}{4}$.

• A. Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I
• B. Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I
• C. Statement-I is true, Statement-II is false
• D. Statement-I is false, Statement-II is true

Answer 1

The correct option is A Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I

$\alpha ,\beta$ are the roots of equation $x^2+2(a-3)x+9=0$, $a\in R$ and $\alpha <6<\beta$.
Since, $a>0$ and $\alpha <6<\beta$
$\Rightarrow f\left(6\right)<0$
$\Rightarrow 36+12(a-3)+9<0$
$\Rightarrow a<\frac{-3}{4}$
Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I
Hence, option A.