Question

How do you factor this equation? 7x²+5x-3

Answer 1

Answer:

Step-by-step explanation:

This is a quadratic expression.  Use the quadratic formula to find the roots, and then once you have the roots, write the corresponding factors.

The coefficients of this quadratic expression are a = 7, b = 5 and c = -3

The discriminant is b^2 - 4ac, or 5^ - 4(7)(-3), or 25 + 84 = 109.  Because this is positive, we know that the expression has two unequal, real roots.

Using the quadratic formula, we now find these roots:

      -b ± √(discriminant)

x = --------------------------------   which here is:

                   2a

      -5 ± √109

x = -----------------

             14

The factors can be found from these two roots.  The first one is

      -5 - √109                  5 + √109

(x - ---------------- )  =  (x + ---------------- )

             14                              14

and the second is

        5 - √109              

(x + ---------------- )  

             14