Question

For what values of ${}^{\prime }{p}^{\prime }$ the equation $(1+p)x^2+2(1+2p)x+(1+p)=0$ has coincident roots ?

• A. 2/3, 0
• B. -2/3, 0
• C. -3/2, 0
• D. None of these

Answer 1

The correct option is B -2/3, 0

Given equation is: $(1+p)x^2+2(1+2p)x+(1+p)=0$

For coincident roots, $D=0$
$\Rightarrow {\left[2(1+2p)\right]}^2-{4(1+p)}^2=0$
$\Rightarrow 1+{4p}^2+4p-1-p^2-2p=0$
$\Rightarrow 3p^2+2p=0$
$\Rightarrow p(3p+2)=0$
$\Rightarrow p=0.-\frac{2}{3}$