Which two values of x are roots of the polynomial below?x2-11x + 15

The two values of roots of the polynomial [tex]x^{2}-11 x+15[/tex] are [tex]\frac{11+\sqrt{61}}{2} \text { or } \frac{11-\sqrt{61}}{2}[/tex]Solution:Given, polynomial expression is [tex]x^{2}-11 x+15[/tex]We have to find the roots of the given expression.In order to find roots, now let us use quadratic formula. [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]Given that [tex]x^{2}-11 x+15[/tex] Here a = 1, b = -11 and c = 15On substituting the values we get,[tex]x=\frac{-(-11) \pm \sqrt{(-11)^{2}-4 \times 1 \times 15}}{2 \times 1}[/tex][tex]\begin{array}{l}{x=\frac{11 \pm \sqrt{121-60}}{2}} \\\\ {x=\frac{11 \pm \sqrt{61}}{2}} \\\\ {x=\frac{11+\sqrt{61}}{2} \text { or } \frac{11-\sqrt{61}}{2}}\end{array}[/tex]Hence, the roots of given polynomial are [tex]\frac{11+\sqrt{61}}{2} \text { or } \frac{11-\sqrt{61}}{2}[/tex]