Question

If one root of the equation $x^2-30x+p=0$ is square of the other, then $p$ is equal to

• A. only $125$
• B. $125,-216$
• C. $125,215$
• D. only $216$

Answer 1

The correct option is B $125,-216$

Given quadratic equation
$x^2-30x+p=0$
Let the roots be $\alpha ,{\alpha }^2$
$\alpha +{\alpha }^2=30$ and ${\alpha }^3=p$
${\alpha }^2+\alpha -30=0$
$(\alpha +6)(\alpha -5)=0$
$\alpha =-6,5$
$\Rightarrow p=-216,125$