Question

Find all the zeros of the equation 12x^2-64=-x^4

Answer 1

Answer: all the zeroes of the above equation will be

(x-4)(x+4)(x-2)(x+2)

Step-by-step explanation:

Since we  have given that

$12x^2-64=-x^4\\\\x^4+12x^2-64=0$

We need to find the zeroes of the above equation.

So, we will use  "Split the middle terms" :

$x^4+12x^2-64=0\\\\x^4+16x^2-4x^2-64=0\\\\x^2(x^2-16)-4(x^2-16)=0\\\\(x^2-4)(x^2-16)=0\\\\x^2-4=0\ or\ x^2-16=0\\\\\text{ "Using }a^2-b^2=(a+b)(a-b)"\\\\x^2-4=x^2-2^2=(x-2)(x+2)\\\\x^2-16=x^2-4^2=(x+4)(x-4)$

So, all the zeroes of the above equation will be

(x-4)(x+4)(x-2)(x+2)