The roots of polynomial are x = 9 , x = -8
Solution:
Given polynomial equation is:
[tex]x^2 - x - 72 = 0[/tex]
We have to find the roots of polynomial equation
Solve by quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-1,\:c=-72[/tex]
[tex]x = \frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\left(-72\right)}}{2\cdot \:1}\\\\Simplify\\\\x = \frac{1 \pm \sqrt{1+288}}{2}\\\\x = \frac{1 \pm \sqrt{289}}{2}\\\\Simplify\\\\x = \frac{1 \pm 17}{2}\\\\We\ have\ two\ roots\\\\x = \frac{1+17}{2} \text{ and } x = \frac{1-17}{2}\\\\x = \frac{18}{2} \text{ and } x = \frac{-16}{2}\\\\x = 9 \text{ and } x = -8[/tex]
Thus, the roots of polynomial are x = 9 , x = -8
