Question

Find the discriminant.

4z^2 + 9 = 0
How many real solutions does the equation have?

Answer 1

To find the discriminant of the quadratic equation \(4z^2 + 9 = 0\), we need to first rewrite it in the standard form \(az^2 + bz + c = 0\). Here, we can identify:

- \(a = 4\)
- \(b = 0\)
- \(c = 9\)

The discriminant \(D\) of a quadratic equation is given by the formula:

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

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

\[
D = 0^2 - 4(4)(9)
\]
\[
D = 0 - 144
\]
\[
D = -144
\]

Since the discriminant \(D\) is negative, the equation \(4z^2 + 9 = 0\) has no real solutions. Instead, it has two complex solutions.

Thus, the answer is:
- The discriminant is \(-144\).
- The equation has 0 real solutions.