Answer to Question #4700 in Functional Analysis for Ash

Question

determine the x intercepts of the function:

f(x) = x^2 -8x -18

Answer 1

Let's consider the following equation:
x^2 - 8x – 18 = 0.
Let's find the discriminant of a given square equation:
D = 8^2 - 4*(-18) = 136 = 4*34, so sqrt(D) = 2sqrt(34).
Let's write down the solution of a given equation using standard formulas for solution of a square equation:
x1 = (8 + 2sqrt(34))/2 = 4 + sqrt(34);
x2 = (8 - 2sqrt(34))/2 = 4 - sqrt(34).
So, the x intercepts of the function are x1 = 4 + sqrt(34) and x2 = 4 - sqrt(34).