Question

Given the roots of $x^2-px+8p-15=0$ are equal, the value of p is equal to

• A. $3,5$
• B. $2,5$
• C. $3,6$
• D. $2,30$

Answer 1

The correct option is D $2,30$

As roots of the equation are equal. Given that,
$x^2-px+8p-15=0$

If roots are equal then discriminant D = 0

$\Rightarrow$ $D=$ $\sqrt{b^2-4ac}=0$

$\Rightarrow$ $\sqrt{(-p^2)-4\times (8p-15)\times 1}=0$

$\Rightarrow$ $\sqrt{p^2-32p+60}=0$

On squaring both sides

$\Rightarrow$ $p^2-32p+60=0$

$\Rightarrow$ $p^2-30p-2p+60=0$

$\Rightarrow$ $p(p-30)-2(p-30)=0$

$\Rightarrow$ $(p-2)(p-30)=0$

$\Rightarrow$ $p=2,30$