Algebra what are the zeros of the function represented by the quadratic expression 2x^2 - 5x -3? ? must show work 

x = 3, x = -1/2

Step-by-step explanation:

Two sure-fire approaches to finding the zeros would be the quadratic formula and /or synthetic division (which would tell you whether or not a possible root actually is a root).

Starting with the q. formula:  a=2, b= -5 and c = -3.  Then the discriminant b^2-4ac is (-5)^2 - 4(2)(-3), or 25+24, or 49.  The square root of this discriminant is 7.  Thus, the roots are:

      -(-5) plus or minus 7    

x = , or x = 3 or x = -2/4 = - 1/2.

                  2(2)

You could just stop here.

Or you could verify that 3 is a zero, using synthetic div.:

3 /   2     -5     -3

              6       3

      2       1       0

Since the remainder is 0, 3 is a zero of the given quadratic expression.  The other zero can be found from rewriting the coefficients 2  1  as 2x + 1 = 0, which gives us x = -1/2 (as expected).