Question

If the equation $x^2-px+216=0$ has one root as a square of the other, find the value of $p$

• A. $42$
• B. $-30$
• C. $36$
• D. $30$

Answer 1

The correct option is A

$42$

$x^2-px+216=0$

Let the roots of the equation be $\alpha ,{\alpha }^2$.

Product of roots $=\frac{c}{a}=\alpha \times {\alpha }^2$

$\Rightarrow {\alpha }^3=216$

$\Rightarrow \alpha =6$

Sum of roots $=\frac{-b}{a}=\alpha +{\alpha }^2=\frac{p}{1}$

$\Rightarrow 6+36=p$

​​​​​​​$\Rightarrow p=42$