Question

Determine $P$, so that the following equation has coincident roots: $t^2+p^2=2(p+1)t$.

Answer 1

Given,

$t^2+p^2=2(p+1)t$

$\Rightarrow t^2-2(p+1)t+p^2=0$

condition for roots to be coincident is,

$b^2-4ac=0$

$[-2(p+1){]}^2=4(1\left)\right(p^2)$

$4(p+1{)}^2=4p^2$

$p^2+1+2p=p^2$

$\Rightarrow p=-\frac{1}{2}$