Question

For what value of $k,(4-k)x^2+2(k+2)x+(8k+1)$ is a perfect square i.e. has equal roots

• A. k = $3$
• B. k = $0$
• C. does not exist
• D. Both A & B

Answer 1

The correct option is D Both A & B

perfect square $=$ equal roots $=\Delta =0$

$\therefore \left(2\right(k+2){)}^2-4(4-k\left)\right(8k+1)=0$

$4(k^2+4+4k)-4(32k+4-8k^2-k)=0$

$\Rightarrow k^2+4+4k-32k-4+8k^2+k=0$

$\Rightarrow 9k^2-27k=0$

$\Rightarrow k^2-3k=0$

$\Rightarrow k(k-3)=0$

$\Rightarrow k=0$ or $k=3$