Question

For what value of k, roots of the quadratic equation \(x^2 + 6x + k =0\) are real and equal?

(A) 12

(B) 9

(C) 10

(D) 6

Answer 1

Correct option is (B) 9

The given quadratic equation is,

\(x^{2}+6 x+k=0\)

Here,

\(a=1, b=6 \text { and } c=k\)

For real and equal roots,

\(D =0\)

\(b^{2}-4 a c =0\)

\((6)^{2}-4 \times 1 \times k=0\)

\(36-4 k =0\)

\(+4 k =+36\)

\(k=\frac{36}{4}\)

\(\therefore k =9\)