MCQ
If the quadratic equations $\text{bx}^2 - 2\sqrt{\text{acx}}+\text{b} = 0$ has equal roots, then :
- A$ 2 b^2= {ac} $
- ✓$ {b}^2= {ac} $
- C$ {b}^2=2 {ac}$
- D$ {b}^2=-{ac}$
✓
Answer
Correct option: B.
$ {b}^2= {ac} $
If the quadratic equation $\text{bx}^2 - 2\sqrt{\text{acx}}+\text{b} = 0$ has equal roots,
then $b^2- 4ac = 0$
$\Rightarrow(- 2\sqrt{\text{ac}})^{2}-4\times\text{b}\times\text{b} = 0$
$\Rightarrow4\text{ac} - 4\text{b}^2$
$\Rightarrow \text{b}^2 = \text{ac}$
then $b^2- 4ac = 0$
$\Rightarrow(- 2\sqrt{\text{ac}})^{2}-4\times\text{b}\times\text{b} = 0$
$\Rightarrow4\text{ac} - 4\text{b}^2$
$\Rightarrow \text{b}^2 = \text{ac}$
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