Question

What are the solutions of the equation x^4 – 5x^2 – 36 = 0? Use factoring to solve.

Answer 1

Answer:

Step-by-step explanation:

The equation is x^4 – 5x^2 – 36 = 0

We will break the middle term:

Firstly multiply the coefficient of x^4 by constant term of the equation:

1*36 = 36

Now find any two numbers whose product is 36 and their sum or difference is equal to 5

9*4 = 36

9-4 = 5

Now,

x^4 – 5x^2 – 36 = 0

x^4-9x^2+4x^2-36=0

Now take the common:

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

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

x²+4=0,

x²= 0-4,

x²=-4,  

Take root on both sides:

√x²=+/-√-4

+/-√-4 = +/-√-1 *√4

√-1 = i

Then +/-√-1 *√4 = √4 i

We know that the root of 4 is 2

Then we can write it as +/-2i

Thus x = 2i , -2i

Now (x^2-9)= 0

x²=0+9

x²=9

Take square root on both sides:

√x²=√9

x=+/-3

x= 3, -3

Therefore the values of x are 2i, -2i, 3 , -3 ....