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

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

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)