Question

For the equation $3x^2+px+3+0$ if one root is square of the other root, then $p=$

• A. $\frac{1}{3}$
• B. $1$
• C. $-6$
• D. $3$

Answer 1

Answer: (C)

$-6$

Solution :-

$3x^2+px+3=0$

Given one root is square of other i.e, $\alpha ,\sqrt{\alpha }$

$\alpha +\sqrt{\alpha }=\frac{-p}{3}$___(1)

and $\alpha .\sqrt{\alpha }=1\Rightarrow {\alpha }^{3/2}=1\Rightarrow \alpha =1$

then (1) becomes

$2=\frac{-p}{3}\Rightarrow p=-6$