Question

Find four solutions to the equation (x² − 9)(x^4 − 16) = 0.

Answer 1

±3, ±2

Explanation:

We have to find all the four roots of the equation
`(x^(2)-9 )(x^(4)-16)`=0.

Now, if product of two factors of an expression a and b is equal to 0 then, either a=0 or b=0

Therefore, from the equation
`(x^(2)-9 )(x^(4)-16)`=0. we can write,

`(x^(2) -9)` =0 ..... (1)

or
`(x^(4) -16) =0` ..... (2)

Now, from equation (1), x² =9, ⇒ x= ±3

Again from equation (2),
`x^(4) =16,`, ⇒x= ±2.

Therefore, the four solutions of x are ±3 and ±2. (Answer)