Question

If $x^2-2Px+8P-15=0$ has equal roots, then $P$ equals

• A. $3$ or $5$
• B. $3$ or $-5$
• C. $-3$ or $5$
• D. $-3$ or $-5$

Answer 1

The correct option is A $3$ or $5$

let the root be $\alpha$ then

$2\alpha =2P\Rightarrow \alpha =P$.....(1)

and

${\alpha }^2=8P-15=8\alpha -15$

${\alpha }^2=3\alpha -5\alpha +15=0$

$\Rightarrow (\alpha -3)(\alpha -5)=0$

$\alpha =3$ or $5$

$P=3$ or $5$