Question

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

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

Answer 1

The correct option is C

1, –5

Step 1:- $x^2+2(k+2)x+9=0$, $\Rightarrow a=1,b=2(k+2),c=9$

$D=4(k+2{)}^2–4(9)=4(k^2+4k-5)$ [$D=b^2-4ac$ ]

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

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

Step 3:- $k^2+4k-5=0$

$\Rightarrow k^2+5k-k-5=0$

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

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

$\Rightarrow k=1ork=-5$