Question

The equation $x^2-2(1+3m)x+7(3+2m)=0$ will have equal roots if $m=2,-\frac{10}{9}.$

If above ststement is true enter ${}^{\prime }{0}^{\prime }$ else enter ${}^{\prime }{1}^{\prime }.$

Answer 1

Given,

$x^2-2(1+3m)x+7(3+2m)=0$

$a=1,b=-2(1+3m),c=7(3+2m)$

The condition for the quadratic equation to have equal roots.

$b^2-4ac=0$

$[-2(1+3m){]}^2-4(1\left)\right[7(3+2m)]=0$

$\Rightarrow 9m^2-8m-20=0$

$(m-2)(m+\frac{10}{9})=0$

$\therefore m=2,-\frac{10}{9}$