Question

Find the smallest zero of f(x+5)

Answer 1

k=13 while x =-10 :)

Explanation:

Answer 2

1. k=13

2. x=-10

EXPLANATION

The given function is

`f(x) = {x}^(2) + 3x - 10`

To find f(x+5), plug in (x+5) wherever you see x.

This implies that:

`f(x) = {(x + 5)}^(2) + 3(x + 5) - 10`

Expand:

`f(x) = {x}^(2) + 10x + 25+ 3x + 15- 10`

Simplify to obtain

`f(x) = {x}^(2) + 13x + 30`

We now compare with,

`f(x) = {x}^(2) + kx + 30`

This implies that:

`k = 13`

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

`{x}^(2) + 13x + 30 = 0`

`{x}^(2) + 10x + 3x + 30 = 0`

`x(x + 10) + 3(x + 10) = 0`

`(x + 3)(x + 10) = 0`

`x = - 10 \: or \: x = - 3`

The smallest zero is -10.