The function f 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=

F (x+5)

just replace all x's with x+5 in first equation

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

f (x+5) = x^2+10x+25+3x+15-10

f (x+5) = x^2+13x+30

compare

f (x) = x^2+3x-10

f (x+5) = x^2+13x+30

now we can set it to zero

f (x+5) = 0

0=x^2+13x+30

factor

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

set each to zero

x+3=0

x=-3

x+10=0

x=-10

-10<-3

smalles zero is x=-10