Question

Solve issuing quadratic techniques
x^4 - 29x^2 + 100 = 0

Answer 1

Define y = x².

Then the given equation may be written as
y² - 29y + 100 = 0
Factorize to obtain
(y - 4)(y - 25) = 0
The solutions are
y = 4 or y = 25

Because y = x², obtain
x² = 4 => x = 2 or x = -2.
x² = 25 => x = 5 or x = -5
The solution for x is 2, -2, 5, -5.
A plot of the function (shown below) verifies that the answer is correct.

Answer: x = 2, -2, 5, -5