MCQ
If the equation $x^2- kx + 1 = 0$ has no real roots, then :
- A$k < -2$
- B$k > 2$
- ✓$-2 < k < 2$
- DNone of these.
✓
Answer
Correct option: C.
$-2 < k < 2$
Since the equation $x^2+ 5kx + 16 = 0$ has no real roots,
$\Rightarrow D < 0$
$\Rightarrow b^2- 4ac > 0$
$\Rightarrow (-k)^2- 4 \times 1 \times 1 < 0$
$\Rightarrow k^2- 4 < 0$
$\Rightarrow k^2 < 4$
$\Rightarrow\text{k}<\sqrt{4}$ or $\text{k}>-\sqrt{4}$
$\Rightarrow k < 2$ or $k > -2$
$\Rightarrow -2 < k < 2$
$\Rightarrow D < 0$
$\Rightarrow b^2- 4ac > 0$
$\Rightarrow (-k)^2- 4 \times 1 \times 1 < 0$
$\Rightarrow k^2- 4 < 0$
$\Rightarrow k^2 < 4$
$\Rightarrow\text{k}<\sqrt{4}$ or $\text{k}>-\sqrt{4}$
$\Rightarrow k < 2$ or $k > -2$
$\Rightarrow -2 < k < 2$
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