Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Find all the zeroes of the equation. x 4 – 6 x 2 – 7 x – 6 = 0

Answer 1

±√7 and ±√6

Explanation:

Let's denote x^2 as y, then the equation becomes:

y^2 - 6y - 7y - 6 = 0

y(y - 6) - 7(y - 6) = 0

(y - 7)(y - 6) = 0

Substituting back y with x^2, we get:

(x^2 - 7)(x^2 - 6) = 0

Solving each factor separately:

x^2 - 7 = 0 or x^2 - 6 = 0

x^2 = 7 or x^2 = 6

x = ±√7 or x = ±√6

Therefore, the zeroes of the equation are ±√7 and ±√6.