<h3>The roots of polynomial are x = 9 , x = -8</h3>
<em><u>Solution:</u></em>
<em><u>Given polynomial equation is:</u></em>
![x^2 - x - 72 = 0](https://tex.z-dn.net/?f=x%5E2%20-%20x%20-%2072%20%3D%200)
We have to find the roots of polynomial equation
<em><u>Solve by quadratic formula</u></em>
![\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}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3Aa%5C%3Aquadratic%5C%3Aequation%5C%3Aof%5C%3Athe%5C%3Aform%5C%3A%7Dax%5E2%2Bbx%2Bc%3D0%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
![\mathrm{For\:}\quad a=1,\:b=-1,\:c=-72](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7D%5Cquad%20a%3D1%2C%5C%3Ab%3D-1%2C%5C%3Ac%3D-72)
![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](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-%5Cleft%28-1%5Cright%29%5Cpm%20%5Csqrt%7B%5Cleft%28-1%5Cright%29%5E2-4%5Ccdot%20%5C%3A1%5Cleft%28-72%5Cright%29%7D%7D%7B2%5Ccdot%20%5C%3A1%7D%5C%5C%5C%5CSimplify%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%20%5Cpm%20%5Csqrt%7B1%2B288%7D%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%20%5Cpm%20%5Csqrt%7B289%7D%7D%7B2%7D%5C%5C%5C%5CSimplify%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%20%20%5Cpm%2017%7D%7B2%7D%5C%5C%5C%5CWe%5C%20have%5C%20two%5C%20roots%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B1%2B17%7D%7B2%7D%20%5Ctext%7B%20and%20%7D%20x%20%3D%20%5Cfrac%7B1-17%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B18%7D%7B2%7D%20%5Ctext%7B%20and%20%7D%20x%20%3D%20%5Cfrac%7B-16%7D%7B2%7D%5C%5C%5C%5Cx%20%3D%209%20%5Ctext%7B%20and%20%7D%20x%20%3D%20-8)
Thus, the roots of polynomial are x = 9 , x = -8
Bye it bye it now dont pass up the opportunity <span />
Answer:
Step-by-step explanation:
-2^2 is -4
-18^2 is -324