To find the value of [tex]\( b^2 - 4ac \)[/tex] for the given quadratic equation [tex]\( 2x^2 + 3x = -1 \)[/tex], follow these steps:
1. Rewrite the equation in standard form:
The standard form of a quadratic equation is [tex]\( ax^2 + bx + c = 0 \)[/tex]. So we need to bring all terms to one side of the equation.
[tex]\[
2x^2 + 3x + 1 = 0
\][/tex]
2. Identify the coefficients:
From the standard form equation [tex]\( 2x^2 + 3x + 1 = 0 \)[/tex]:
[tex]\[
a = 2, \quad b = 3, \quad c = 1
\][/tex]
3. Calculate the discriminant:
The discriminant of a quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] is given by [tex]\( b^2 - 4ac \)[/tex].
Substituting the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[
b^2 - 4ac = 3^2 - 4 \cdot 2 \cdot 1
\][/tex]
4. Perform the arithmetic operations:
[tex]\[
b^2 - 4ac = 9 - 8 = 1
\][/tex]
Hence, the value of [tex]\( b^2 - 4ac \)[/tex] for the equation [tex]\( 2x^2 + 3x = -1 \)[/tex] is [tex]\( 1 \)[/tex].
So, the correct answer is:
[tex]\[
1
\][/tex]
