Question

Factor this equation using the Zero product property , What are the x-intercepts?: f(x)=2x^2+5x-3

Answer 1

x = 1/2

x = -3

Explanation:

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

Factor

Zero Product Property

X-Intercepts

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To find the x intercepts, we need to first factor our given polynomial. The quickest trick I use to factor is to find two numbers that multiply to c (in this case -3) and the same two numbers that add to b (in this case 5).

The two numbers would be -1 and 3, but along with 2x to help out.

Therefore the binomial for this factor is :

`(2x-1)(x+3)`

Now to solve the x-intercepts, we separate the binomials into an algebraic expressions :

2x - 1 = 0

x + 3 = 0

Isolate for x in both of them :

2x - 1 = 0

Add 1 to both sides :

2x = 1

Divide both sides by 2 :

x = 1/2

x + 3 = 0

Subtract 3 from both sides :

x = -3