MCQ
If the equation $9x^2+ 6kx + 4 = 0$ has equal roots then $k = ?$
- A$2$ or $0$
- B$-2$ or $0$
- ✓$2$ or $-2$
- D$0$ only
✓
Answer
Correct option: C.
$2$ or $-2$
Since the roots of the equation $9x^2+ 6kx + 4 = 0$ are equal,
$D = 0$
$ \Rightarrow b^2-4 a c=0 $
$ \Rightarrow(6 k)^2-4 \times 9 \times 4=0 $
$ \Rightarrow 36 k^2-144=0 $
$ \Rightarrow 36 k^2=144 $
$ \Rightarrow k^2=4 $
$\Rightarrow\text{k}=\pm2$
$D = 0$
$ \Rightarrow b^2-4 a c=0 $
$ \Rightarrow(6 k)^2-4 \times 9 \times 4=0 $
$ \Rightarrow 36 k^2-144=0 $
$ \Rightarrow 36 k^2=144 $
$ \Rightarrow k^2=4 $
$\Rightarrow\text{k}=\pm2$
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