Question

Please help thats the answer but i dont know
how to get it

Answer 1

Here we have to find zeroes of the given function.

Let's start solving!

`f(x) = x ^(3) + 9x ^(2) + 6x - 16`

• To find x-intercept or zeroes, Substitute f(x) =0

`0 = x ^(3) + 9x ^(2) + 6x - 16`

• Move the expression to the left hand side and change its sign

`0 - x ^(3) - 9x ^(2) - 6x + 16 = 0`

`- x ^(3) + x ^(2) - 10x ^(2) + 10x - 16x + 16 = 0`

`- x ^(2) (x - 1) - 10x(x - 1) - 16(x - 1) = 0`

`- (x - 1) * (x ^(2) + 10x + 16) = 0`

`- (x - 1) * (x ^(2) + 8x + 2x + 16) = 0`

`- (x - 1) * (x * (x + 8) + 2(x + 8)) = 0`

`- (x - 1) * (x + 8) * (x + 2) = 0`

`(x - 1)(x + 8)(x + 2) = 0`

`x - 1 = 0 \\ x + 8 = 0 \\ x + 2 = 0`

`x = 1 \\ x = - 8 \\ x = - 2`

`x_(1) = 8, x_(2) = - 2, x_(3) = 1`