Sure! Let's find the discriminant of the quadratic equation [tex]\(0 = 2x^2 + 3x - 5\)[/tex].
The general form of a quadratic equation is [tex]\(ax^2 + bx + c = 0\)[/tex], where [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are constants.
In our specific equation, we have:
[tex]\[ a = 2 \][/tex]
[tex]\[ b = 3 \][/tex]
[tex]\[ c = -5 \][/tex]
The discriminant [tex]\(\Delta\)[/tex] of a quadratic equation is given by the formula:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
Now, we will substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] into the formula to compute the discriminant:
[tex]\[ \Delta = 3^2 - 4(2)(-5) \][/tex]
Perform the calculations step-by-step:
1. Calculate [tex]\(b^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
2. Calculate [tex]\(4ac\)[/tex]:
[tex]\[ 4(2)(-5) = 4 \cdot 2 \cdot -5 = -40 \][/tex]
3. Now, evaluate the entire expression:
[tex]\[ \Delta = 9 - (-40) \][/tex]
4. Simplify the expression:
[tex]\[ \Delta = 9 + 40 \][/tex]
[tex]\[ \Delta = 49 \][/tex]
Thus, the discriminant of the quadratic equation [tex]\(0 = 2x^2 + 3x - 5\)[/tex] is [tex]\(49\)[/tex]. Therefore, the correct answer is:
[tex]\[ \boxed{49} \][/tex]
