Question

Which two values of x are roots of the polynomial below? x^2-3x+5

Answer 1

Given:

Polynomial $x^2-3x+5$

To find:

The values of x.

Solution:

$x^2-3x+5=0$

Quadratic equation formula:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here $a=1, b=-3, c=5$.

Substitute the values in the formula, we get

$x=\frac{-(-3) \pm \sqrt{(-3)^{2}-4 \cdot 1 \cdot 5}}{2 \cdot 1}$

$x=\frac{3 \pm \sqrt{9-20}}{2}$

$x=\frac{3 \pm \sqrt{-11}}{2}$

$x=\frac{3 - \sqrt{-11}}{2} \ \text{and} \ x=\frac{3 + \sqrt{-11}}{2}$

Option E and option F are the roots of the polynomial.

The values of x are $x=\frac{3 - \sqrt{-11}}{2} \ \text{and} \ x=\frac{3 + \sqrt{-11}}{2}$.