Question

Among the following, find the values of $x$ that are real and satisfy the equation $2x^2-5x-2=0$

• A. $1$ and $4$
• B. $-\frac{5}{4}+\frac{\sqrt{41}}{4}$ and $-\frac{5}{4}-\frac{\sqrt{41}}{4}$
• C. $\frac{5}{4}+\frac{\sqrt{41}}{4}$ and $\frac{5}{4}-\frac{\sqrt{41}}{4}$
• D. No real solutions

Answer 1

Answer: (C)

$\frac{5}{4}+\frac{\sqrt{41}}{4}$ and $\frac{5}{4}-\frac{\sqrt{41}}{4}$

For finding the values of $x$ which satisfy the above equation, we solve the equation for $x$.

$2x^2-5x-2=0$

$\Rightarrow x=\frac{5\pm \sqrt{25+16}}{4}$

$\Rightarrow x=\frac{5\pm \sqrt{41}}{4}$

$\Rightarrow x=\frac{5+\sqrt{41}}{4},\frac{5-\sqrt{41}}{4}$