Question

Find what value of P equation px2+6x+4p=o has product of root equal to the sum of the roots

Answer 1

We need to recall the following concept for the roots of a quadratic equation.

If $\alpha ,\beta$ are the roots of a quadratic equation $ax^{2} +bx+c=0$, then

• Sum of the roots:  $\alpha +\beta =-\frac{b}{a}$
• Product of the roots:  $\alpha \beta =\frac{c}{a}$

Given:

$px^{2} +6x+4p=0$

The product of roots is equal to the sum of the roots.

Here, $a=p$, $b=6$ and $c=4p$

Then,

the sum of the roots$=-\frac{6}{p}$

the product of the roots $=\frac{4p}{p}=4$

It is given that the product of roots is equal to the sum of the roots.

$-\frac{6}{p}=4$

$p=-\frac{6}{4}$

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

Hence, the value of $p$ is $-\frac{3}{2}$ .