Question

How many real solutions does the following quadratic equation have? 25x ^ 2 + 60x + 36 = 0 (1 point) solution(s)

Answer 1

To determine the number of real solutions for the quadratic equation \( 25x^2 + 60x + 36 = 0 \), we can use the discriminant \( D \) from the quadratic formula, which is given by:

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

Here, in the equation \( ax^2 + bx + c = 0 \), we have:

- \( a = 25 \)
- \( b = 60 \)
- \( c = 36 \)

Now, we substitute these values into the formula for the discriminant:

\[
D = (60)^2 - 4(25)(36)
\]

Calculating \( (60)^2 \):

\[
(60)^2 = 3600
\]

Now, calculating \( 4(25)(36) \):

\[
4 \times 25 = 100 \quad \text{and} \quad 100 \times 36 = 3600
\]

Now substituting these values back into the discriminant:

\[
D = 3600 - 3600 = 0
\]

Since the discriminant \( D = 0 \), this indicates that the quadratic equation has exactly one real solution (or one repeated real root).

Thus, the answer is that the equation \( 25x^2 + 60x + 36 = 0 \) has **1 real solution**.