determine the x-intercepts of the function f(x) = 12x^2 + 5x - 2

Answer 1

When you find x intercepts of a quadratic function; you will factor the function by making y= 0 Factoring 12x²-5x-2 

The first term is,  12x²  its coefficient is  12 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  -2 

Step-1 : Multiply the coefficient of the first term by the constant  12 • -2 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is  -5 .

	-24	+	1	=	-23
	-12	+	2	=	-10
	-8	+	3	=	-5	That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -8  and  3 

                     12x² - 8x + 3x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                    4x • (3x-2)

             Add up the last 2 terms, pulling out common factors :

                     1 • (3x-2)

Step-5 : Add up the four terms of step 4 :

                    (4x+1)  •  (3x-2)

             Which is the desired factorization

Step-6 Since (4x+1)  •  (3x-2) = 0

4x+1 = 0 and 3x – 2 =0

When you solve the equations above for x; you get your answer

Hope that helps