Question

Which two values of x are roots of the polynomial below? x^2-11x+15

Answer 1

${x}^{2} - 11x + 15 = 0 \\ \Rightarrow x = \frac{11\pm \sqrt{ { - 11}^{2}+ 4 \times 15} }{2} = \frac{11\pm \sqrt{61} }{2} \\ \Rightarrow B, D$

Answer 2

Answer:  The correct options are

(B) $x=\dfrac{11+\sqrt{61}}{2}.$

(D) $x=\dfrac{11-\sqrt{61}}{2}.$

Step-by-step explanation:  We are given to select the values of x that are the roots of the following polynomial :

$x^2-11x+15.$

The quadratic equation formed by the given polynomial will be

$x^2-11x+15=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

we know that

the solution set of a quadratic equation $ax^2+bx+c=0,~~a\neq 0$ is given by

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

From equation (i), we have

a = 1, b = -11  and  c = 15.

Therefore, the roots of equation (i) will be given by

$x=\dfrac{-(-11)\pm\sqrt{(-11)^2-4\times1\times15}}{2\times1}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{121-60}}{2}\\\\\\\Rightarrow x=\dfrac{11\pm\sqrt{61}}{2}.$

Thus, the roots of the given polynomial are

$x=\dfrac{11+\sqrt{61}}{2},~~~~~x=\dfrac{11-\sqrt{61}}{2}.$

Options (B) and (D) are CORRECT.