Question

What are the solutions of the equation x4 – 5x2 – 36 = 0? use factoring to solve.

Answer 1

X^4 - 5x^2 - 36 = 0
(x^2 - 9)(x^2 + 4) = 0
(x-3)(x+3)(x-2)(x+2) = 0

x = -3, -2, 2, 3

Answer 2

Answer:

x = 3, -3, 2i and -2i where i is an imaginary number.

Step-by-step explanation:

We can express the equation $x^4-5x^2-36=0$ as $(x^2)^2-5x^2-36=0$, and we can make $y = x^2$. So, we have the equation $y^2-5y-36=0$; to find the solutions of this last equation, we should find two numbers such that these numbers sum up to -5 and multiplied result in -36, these numbers are -9 and 4. Therefore $y^2-5y-36=0$ is equivalent to $(y-9)(y+4)=0$, but $y = x^2$, so, $(x^2-9)(x^2+4)=0$, i.e., $(x+3)(x-3)(x^2+4)=0$. This last product is equal to zero when x = 3, x = -3 or $x^2=-4$, $x=\pm\sqrt{-4}$, i.e., $x=\pm2i$. Therefore the solutions of the equation $x^4-5x^2-36=0$ are x = 3, -3, 2i and -2i where i is an imaginary number.