Answer:
x = 3, x = -1/2
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).