Question

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

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

Answer 1

The correct option is A

1, 4

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

Step 2:- The roots of quadratic equation are real and equal only when $D=0$.

$k^2+4-5k=0$

$\Rightarrow k^2-5k+4=0$
$k^2-k-4k+4=0$
$k(k-1)-4(k-1)=0$
$(k-1)(k-4)=0$

Step 3:- $k=4or1$