The required roots of the polynomial is x = 9 and x = -8 .
Given that ,
Polynomial equation = [tex]f(x) = x^{2} -x-72= 0[/tex].
We have to find ,
The roots of the polynomial equation.
According to the question,
Quadratic equations are the polynomial equations of degree 2 in one variable of type [tex]f(x) = ax^{2} +bx+c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.
The values of x satisfying the quadratic equation are the roots of the quadratic equation (α,β).
The quadratic equation will always have two roots.
Then ,
[tex]f(x) = x^{2} -x-72=0\\[/tex]
For the roots of equation factorize the given polynomial equation,
[tex]x^{2} -x - 72= 0 \\x^{2} -9x+8x-72 = 0 \\x (x-9) + 8(x-9) = 0\\(x-9) (x+8) = 0[/tex]
So, x - 9 = 0 = x = 9
Or x + 8 = 0 = x = -8
The roots of the equation is ( 9, -8 ).
Hence, The required roots of the polynomial is x = 9 and x = -8 .
For the more information about Quadratic equations click the link given below.
https://brainly.com/question/17177510
