Question

If one of the root of the equation $4x^2-15x+4p=0$ is the square of the other then the value of $p$ is

• A. $125/64$
• B. $-27/8$
• C. $-125/8$
• D. $\frac{27}{8}$,$-\frac{125}{64}$

Answer 1

The correct option is D $\frac{27}{8}$,$-\frac{125}{64}$

Given that $\alpha ,{\alpha }^2$ are the roots of given quadratic equation.

So, $\alpha +{\alpha }^2=\frac{15}{4}$ and ${\alpha }^3=\frac{4p}{p}=4$

$\Rightarrow \alpha +{\alpha }^2=\frac{15}{4}$

$\Rightarrow 4{\alpha }^2+4\alpha =15$

$\Rightarrow 4{\alpha }^2+4\alpha -15=0$

On solving we get,

$\Rightarrow \alpha =\frac{3}{2},\frac{-5}{2}$

Therefore, $\Rightarrow {\alpha }^3=\frac{27}{8},\frac{-125}{8}$