Question

What are the roots of the polynomial equation?

x2−x−72=0

Answer 1

The roots of polynomial are x = 9 , x = -8

Solution:

Given polynomial equation is:

`x^2 - x - 72 = 0`

We have to find the roots of polynomial equation

Solve by quadratic formula

`\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=(-b\pm √(b^2-4ac))/(2a)`

`\mathrm{For\:}\quad a=1,\:b=-1,\:c=-72`

`x = (-\left(-1\right)\pm √(\left(-1\right)^2-4\cdot \:1\left(-72\right)))/(2\cdot \:1)\\\\Simplify\\\\x = (1 \pm √(1+288))/(2)\\\\x = (1 \pm √(289))/(2)\\\\Simplify\\\\x = (1 \pm 17)/(2)\\\\We\ have\ two\ roots\\\\x = (1+17)/(2) \text{ and } x = (1-17)/(2)\\\\x = (18)/(2) \text{ and } x = (-16)/(2)\\\\x = 9 \text{ and } x = -8`

Thus, the roots of polynomial are x = 9 , x = -8