Question

Which two values of x are roots of the polynomial below? x2 - 11x + 13

Answer 1

Answer-

The values of x, which are the roots of the polynomial are

$\dfrac{11+ \sqrt{69}}{2},\ \dfrac{11- \sqrt{69}}{2}$

Solution-

The given polynomial,

$=x^2 - 11x + 13$

We know that,

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here,

a = 1, b = -11, c = 13

Putting the values,

$x=\dfrac{-(-11)\pm \sqrt{(-11)^2-4\times 1\times 13}}{2\times 1}$

$=\dfrac{11\pm \sqrt{121-52}}{2}$

$=\dfrac{11\pm \sqrt{69}}{2}$

$\therefore x=\dfrac{11+ \sqrt{69}}{2},\ \dfrac{11- \sqrt{69}}{2}$