Question

Solve 2x2−5x−3=0 and show your work

Answer 1

Solve 2x^2 − 5x − 3 = 0.

Method 1 — factoring:
Try to factor as (2x + a)(x + b) with ab = −3 and 2b + a = −5.
We find (2x + 1)(x − 3) = 2x^2 − 6x + x − 3 = 2x^2 − 5x − 3.
Set each factor to zero:
2x + 1 = 0 → x = −1/2
x − 3 = 0 → x = 3

Method 2 — quadratic formula (check):
x = [5 ± √( (−5)^2 − 4·2·(−3) )] / (2·2)
= [5 ± √(25 + 24)] / 4
= [5 ± √49] / 4
= [5 ± 7] / 4
gives x = (5+7)/4 = 3 and x = (5−7)/4 = −1/2.

Solutions: x = 3 and x = −1/2.