Can you help me find the zeros of a function using factoring?

Question

g(x)=2x²+x-10

Answer 1

To find the zeroes, set the function equal to 0 and solve.

2x² + x - 10 = 0

 

To factor a quadratic with a leading coefficient that is not 1, you multiply the first and last coefficients, and find it's factors that add to the middle coefficient. Here, we have 2*(-10) = -20, and you want the factors that add up to 1.

Some factors you might choose are -2 & 10, -5 & 4, or 1 & -20. There are others, but find the pair that add to 1. For purposes here I'll call them A and B.

 

(There are other ways to do the next part, but they don't translate to typed solutions well.)

 

Since your A and B sum to 1, and your middle term is 1x, you can split it into two terms:

2x² + Ax + Bx - 10 = 0

Now you can factor this by grouping: factor out the common factor between your first two terms, then again for the second two terms. You should be left with a common binomial factor between the two, which you can then factor out to get a binomal product [i.e (x+2)(x-5) {not the right answer!}]

 

Set each binomal factor = 0, and solve, and you should get your two answers. To help you out, one of the answers should be 2.

 

Good luck!

Answer 2

What are factors of the first term

 

They are 2x and x

 

What are the possible factors of the last term and what combination will give you the middle term

 

One possible combination is 5 and -2

 

5 * x          =5x

2x * -2       =-4x

 

Combining these we have x  so this seems to work

 

(2x + 5)(x -2)  = 0

 

2x + 5 =0

 

2x = -5

x = -5/2

 

x - 2 =0

x = 2