Question

Find the real zeros of the following function, and plot them on the graph. f(x)=(x^4-16)(x^2+3x-18)

Answer 1

the 0 are 2, 3 and -6. ....

Answer 2

Given function,

`f(x)=(x^4-16)(x^2+3x-18)`

`=((x^2)^2-(4)^2)(x^2+(6-3)x-18)`

`=(x^2-4)(x^2+4)(x^2+6x-3x-18)`

`=(x-2)(x+2)(x^2-(2i)^2)(x(x+6)-3(x+6))`

`=(x-2)(x+2)(x+2i)(x-2i)(x-3)(x+6)`

For zeros of function f(x),

f(x) = 0

`\implies (x-2)(x+2)(x+2i)(x-2i)(x-3)(x+6)=0`

By zero product property,

We get,

x = 2, -2, -2i, 2i, 3, -6

Hence, the real roots of f(x) are 2, -2, 3, -6.

Also, the roots lie at the point where a function intersects the x-axis.

Hence, the positions of the roots of f(x) in the graph are ,

(2, 0), (-2, 0), (3, 0) and (-6, 0)