To determine the value of the discriminant for the quadratic equation [tex]\( 2x^2 + 11x + 5 = 0 \)[/tex], we'll use the discriminant formula:
[tex]\[ \Delta = b^2 - 4ac \][/tex]
where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are the coefficients of the quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex].
For this quadratic equation:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 11 \)[/tex]
- [tex]\( c = 5 \)[/tex]
Now, substituting these values into the discriminant formula:
[tex]\[ \Delta = 11^2 - 4 \cdot 2 \cdot 5 \][/tex]
First, calculate [tex]\( 11^2 \)[/tex]:
[tex]\[ 11^2 = 121 \][/tex]
Next, calculate [tex]\( 4 \cdot 2 \cdot 5 \)[/tex]:
[tex]\[ 4 \cdot 2 \cdot 5 = 40 \][/tex]
Now, subtract the second result from the first:
[tex]\[ \Delta = 121 - 40 \][/tex]
[tex]\[ \Delta = 81 \][/tex]
Therefore, the value of the discriminant for the given quadratic equation is [tex]\( \Delta = 81 \)[/tex]. The correct answer is:
81
