Answer:
±3, ±2
Step-by-step explanation:
We have to find all the four roots of the equation [tex](x^{2}-9 )(x^{4}-16)[/tex]=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 [tex](x^{2}-9 )(x^{4}-16)[/tex]=0. we can write,
[tex](x^{2} -9)[/tex] =0 ..... (1)
or [tex](x^{4} -16) =0[/tex] ..... (2)
Now, from equation (1), x² =9, ⇒ x= ±3
Again from equation (2), [tex]x^{4} =16,[/tex], ⇒x= ±2.
Therefore, the four solutions of x are ±3 and ±2. (Answer)
