Question

What is the value of the discriminant for the quadratic equation 9h
2
−6=7h?

0

−167

265

−216

Answer 1

To find the value of the discriminant for the quadratic equation \(9h^2 - 6 = 7h\), we first need to rearrange it into the standard form of a quadratic equation, which is \(ax^2 + bx + c = 0\).

1. Rearranging the given equation:
\[
9h^2 - 7h - 6 = 0
\]

Here, the coefficients are:
- \(a = 9\)
- \(b = -7\)
- \(c = -6\)

2. The discriminant \(D\) of a quadratic equation is given by the formula:
\[
D = b^2 - 4ac
\]

3. Substituting in our values:
\[
D = (-7)^2 - 4(9)(-6)
\]
\[
D = 49 - 4(9)(-6)
\]
\[
D = 49 - 4 \cdot 9 \cdot -6
\]
\[
D = 49 + 216
\]
\[
D = 265
\]

Thus, the value of the discriminant is \(265\).