Question

Find ${}^{\prime }{a}^{\prime }$ for which $a^2{x}^2+2(a+1)x+4=0$ coincident roots.

Answer 1

$a^2{x}^2+2(a+1)x+4=0$

condition for coincident roots $b^2=4ac$

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

$4(a+1{)}^2=4(a^2\left)\right(4)$

$a^2+1+2a=4a^2$

$3a^2-2a-1=0$

$(a-1)(3a+1)=0$

$a=1,-\frac{1}{3}$