Question

For what values of 'k', the equation $x^2+2(k-4)x+2k=0$ has equal roots?

• A. $8,2$
• B. $6,4$
• C. $12,2$
• D. $10,4$

Answer 1

The correct option is A $8,2$

As eq${}^n$ has equal roots

$\Rightarrow D=0$

$\Rightarrow {\left[2\right(k-4\left)\right]}^2-4\times 2k\times 1=0$

$\Rightarrow k^2-8k+16-2k=0$

$\Rightarrow k^2-10k+16=0$

$\Rightarrow (k-2)(k-8)=0$

$\Rightarrow k=8,2$