Question

If $a>0$ , $b>0$, then the roots of the equation $a-bx-x^2=0$ are

• A. both positive
• B. both negative
• C. of opposite sign and numerically greater root is positive
• D. of opposite sign and numerically greater root is negative

Answer 1

Answer: (D)

of opposite sign and numerically greater root is negative

$-x^2-bx+a=0\Rightarrow x^2+bx-a=0.$
Product of roots $=-a<0$
And sum of roots $=-b<0$
$\alpha \times \beta <0$ and
$\alpha +\beta <0$
$\therefore$ The root greater in magnitude is negative
Answer is D