Question

What is the value of the discriminant for the quadratic equation 4n
2
=5n+8?

153

−16

−103

0

Answer 1

To find the value of the discriminant for the quadratic equation \(4n^2 = 5n + 8\), we first need to rearrange the equation into the standard quadratic form, which is \(ax^2 + bx + c = 0\).

Starting with the given equation:

\[
4n^2 - 5n - 8 = 0
\]

Here, the coefficients are:
- \(a = 4\)
- \(b = -5\)
- \(c = -8\)

The discriminant \(D\) is calculated using the formula:

\[
D = b^2 - 4ac
\]

Substituting the values of \(a\), \(b\), and \(c\):

\[
D = (-5)^2 - 4(4)(-8)
\]
\[
D = 25 - 4(4)(-8)
\]
\[
D = 25 - (-128)
\]
\[
D = 25 + 128
\]
\[
D = 153
\]

Thus, the value of the discriminant for the quadratic equation \(4n^2 = 5n + 8\) is \(\boxed{153}\).