Question

Find the value of $k$ for the quadratic equation $x^2-2\left(k+1\right)x+k^2=0$ has real and equal roots.

Answer 1

Given $x^2-2(k+1)x+k^2=0$ has real and equal roots

As we know that

for a quadratic equation to have real and equal roots ,discriminant should be zero

$⟹(-2(k+1){)}^2-4(1\left)\right(k^2)=0$

$⟹(k+1{)}^2-k^2=0$

$⟹2k+1=0$

$⟹k=-\frac{1}{2}$