Question

If $\alpha ,{\alpha }^2$ are the roots of the equation $x^2-90x+k=0$, find sum of all possible values of k.

• A. 729
• B. 1000
• C. -729
• D. -271

Answer 1

The correct option is D

-271

$\alpha +{\alpha }^2=90$
${\alpha }^2+\alpha -90=0$
$(\alpha -9)(\alpha -10)=0$
$\alpha =9$ or $\alpha =-10$

when $\alpha =9$
9,81 are the roots
$\Rightarrow k=729$

When $\alpha =-10$
$-10,100$ are the roots
$\Rightarrow k=-1000$
$\Rightarrow$ Sum of all possible values of $k=-1000+729$
= -271