To find the discriminant of the quadratic equation [tex]\(0=2x^2+3x-5\)[/tex], we need to use the formula for the discriminant of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex]. The formula for the discriminant [tex]\(\Delta\)[/tex] is given by:
[tex]\[
\Delta = b^2 - 4ac
\][/tex]
Here, the coefficients from the equation [tex]\(0 = 2x^2 + 3x - 5\)[/tex] are:
[tex]\[
a = 2, \quad b = 3, \quad c = -5
\][/tex]
Now, let's substitute these values into the discriminant formula:
1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
b^2 = 3^2 = 9
\][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[
4ac = 4 \times 2 \times (-5) = 8 \times (-5) = -40
\][/tex]
3. Substitute the values into the discriminant formula:
[tex]\[
\Delta = b^2 - 4ac = 9 - (-40)
\][/tex]
4. Simplify the expression:
[tex]\[
\Delta = 9 + 40 = 49
\][/tex]
Therefore, the discriminant of the quadratic equation [tex]\(0=2x^2+3x-5\)[/tex] is 49. The correct answer is 49.
