The function is defined by f (x) = x^2+3x-10

if f (x+5) = x^2 + kx+30, k=

find the smallest zero of f (x+5). x=

First you put (x+5) into the initial function wherever you see x so it becomes

(x+5) ^2+3 (x+5) - 10=x^2+kx+30

(x^2+5x+25) + (3x+15) - 10 simplified left side

x^2+8x+30 fully simplified left side

thus k=8

x^2+8x+30=0 to find 0s

-4 + 3.7416573867739i

-4 - 3.7416573867739i

these are the roots you find after using the quadratic formula

the second one is the smallest