Question

Which is a zero of the quadratic function f(x) = 4x2 + 24x + 11?

Answer 1

set to zero
0=4x^2+24x+11
factor
use ac method
muliplty 4 and 11
44
what 2 numbers multily to get 44 and ad to get 24?
2 and 22
0=4x^2+2x+22x+11
0=(4x^2+2x)+(22x+11)
0=2x(2x+1)+11(2x+1)
0=(2x+11)(2x+1)
set to zero

2x+11=0
2x=-11
x=-11/2

2x+1=0
2x=-1
x=-1/2



x=-11/2 and -1/2

Answer 2

4x^2 + 24x + 11 = 0

4x^2 + 2x + 22x + 11 = 0

4x(x + 0.5) + 22(x + 0.5) = 0

(4x + 22) (x + 0.5) = 0

x+5 = 0 gives x = -0.5
and
4x + 22 = 0 gives x = -5.5


so solution set is (-0.5, -5.5)