Question

If the equation $x^2+2(k+2)x+9k=0$ has equal roots, then values of k are __________.

• A. –1 or 5
• B. –1 or –4
• C. 1 or 4
• D. 1 or –5

Answer 1

The correct option is C 1 or 4

Step 1:- For, $x^2+2(k+2)x+9k=0$, value of discriminant $D=\left[2\right(k+2){]}^2–4(9k)=4(k^2+4-5k)$

Step 2:- The roots of quadratic equation are real and equal only when $D=0$
$k^2+4-5k=0$
$\Rightarrow k^2-5k+4=0$
$\Rightarrow k^2-k-4k+4=0$
$\Rightarrow k(k-1)-4(k-1)=0$
$\Rightarrow (k-1)(k-4)=0$

Step 3:- $k=4or1$