Question

Find the nature of root
$x^2+2x-1=0$

• A. Real
• B. Irrational
• C. Complex
• D. None

Answer 1

Answer: (B)

Irrational

$x^2+2x-1=0,a=1,b=2,c=-1$

Let $\alpha ,\beta$ be the roots of the given quadratic equations
$x=\frac{-b\pm \sqrt{2^2-4ac}}{2a}=\frac{-2\pm \sqrt{4+4}}{2}$
$=\frac{-2\pm 2\sqrt{2}}{2}=1\pm \sqrt{2}$

Then, $\alpha =1+\sqrt{2}$ and $\beta =1-\sqrt{2}$ are irrational.
Hence, both roots are irrational.