Question

If a < 0 then the inequality $a{x}^2$-2x + 4 > 0 has the solution represented by

• A. > x >
• B. x <
• C. x < 2
• D. 2 > x >

Answer 1

The correct option is A

> x >

$a{x}^2$ - 2x + 4 > 0

$\Rightarrow x=\frac{2\pm \sqrt{4-16a}}{2a}\Rightarrow x=\frac{1\pm \sqrt{1-4a}}{a}$

$\therefore \frac{1-\sqrt{1-4a}}{a}$ < x < $\frac{1+\sqrt{1-4a}}{a}$