Question

Determine the zero(s) of the quadratic function y=6x2+13x+5
. Show all steps.

Answer 1

We solve 6x^2 + 13x + 5 = 0.

Factor:
6x^2 + 13x + 5 = 6x^2 + 10x + 3x + 5
= (6x^2 + 10x) + (3x + 5)
= 2x(3x + 5) + 1(3x + 5)
= (2x + 1)(3x + 5).

Set each factor to zero:
2x + 1 = 0 → x = -1/2
3x + 5 = 0 → x = -5/3

(Checking with the quadratic formula: x = [-13 ± sqrt(13^2 − 4·6·5)]/(2·6) = [-13 ± 7]/12 gives the same roots.)

Zeros: x = -1/2 and x = -5/3.