To find the sum of the roots of the quadratic equation [tex]\(2x^2 + 3x - 9 = 0\)[/tex], we use a property from algebra known as Vieta's formulas. Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.
For a quadratic equation of the form [tex]\(ax^2 + bx + c = 0\)[/tex], the sum of the roots [tex]\(r_1\)[/tex] and [tex]\(r_2\)[/tex] is given by:
[tex]\[
r_1 + r_2 = -\frac{b}{a}
\][/tex]
Now, for the quadratic equation [tex]\(2x^2 + 3x - 9 = 0\)[/tex]:
- [tex]\(a = 2\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = -9\)[/tex]
Using the formula to find the sum of the roots:
[tex]\[
r_1 + r_2 = -\frac{b}{a} = -\frac{3}{2}
\][/tex]
Hence, the sum of the roots of the equation [tex]\(2x^2 + 3x - 9 = 0\)[/tex] is:
[tex]\[
-\frac{3}{2}
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{-\frac{3}{2}} \)[/tex].
