Question

If the quadratic equation $p{x}^2-2\sqrt{5}px+15=0$,has two roots then find the value of p.

Answer 1

The given quadratic equation is, $p{x}^2-2\sqrt{5}px+15=0$

This is of the form $a{x}^2+bx+c=0$

where, $a=p,b=-2\sqrt{5}p,c=15$

We have, $D=b^2-4ac$

$=(-2\sqrt{5}p{)}^2-4\times p\times 15$

$=20p^2-60p$

=$20p(p-3)$

For real and equal roots,we must have:D=0, $\Rightarrow 20p(p-3)=0$

$\Rightarrow p=0,p=3$

p=0, is not possible as coefficient of $x^2$ cannot be 0.
Hence,3 is the required value of p.