Question

Determine the zeros of each function by factoring:

a. f(x)=-2x^2-5x+12
b. f(x)=2x^2-3x-2
c. f(x)=x^2-10x+24

I have been trying to figure these out for awhile and am stuck. Please and Thank you for help.

Answer 1

what method have you learned ?

The last one is trivial.
What two numbers have a sum of -10 and a product of 24 ?
I would "guess" at -6 and -4
So x = -6 or x = -4

One foolproof method, but not necessarily the best, is decomposition.
multiply the coefficients of the x^2 term and the constant
---- 2(-2) = -4
Now think of two numbers that add have a product of -4 and a sum of -3.
I would say -4 and +1 would do it
so let's replace the middle term with -4x and x
2x^2 - 3x - 2
= 2x^2 - 4x + x - 2
= 2x(x - 2) + (x-2)
= (x - 2)(2x + 1)

so the zeros are 2 and -1/2

apply the same method for the first one, let me know how you made out