Question

Algebraically determine the x-intercepts of this function. Please show work.

Y=x^4 - 10x^2 + 9

Answer 1

To determine x intercept, put y=0

x^4 - 10x^2 + 9 = 0

x^4 - 9x^2 - x^2 + 9 = 0

x^2(x^2 - 9) - 1(x^2 - 9) = 0

(x^2 - 9)(x^2-1) =0

x^2 - 9 = 0
⇒ x^2 = 9
⇒x = +3, -3

x^2 - 1 = 0
x^2 = 1
x = +1, -1

X intercepts are -3, -1, 1, 3