Question

Two roots of the cubic equation $x^3-5x^2-ax+45=0$ are real and additive inverse of each other then a is equal to

• A. 7
• B. 9
• C. 10
• D. 11

Answer 1

Answer: (B)

Let the roots are $\alpha ,-\alpha ,\beta$
$\text{ S.O.R. }=\alpha -\alpha +\beta =5\Rightarrow \beta =5$
$\text{ P.O.R. }=\alpha (-\alpha )\beta =-45\Rightarrow {\alpha }^2=9$
$\Rightarrow \alpha =3$
$\text{ Now, }-a=3(-3)+3(5)+3(-5)$
$-a=-9$
$a=9$