Question

How many real solutions does the following quadratic equation have? 25x2+60x+36=025x2+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 method.

The general form of a quadratic equation is given by \( ax^2 + bx + c = 0 \), where:
- \( a = 25 \)
- \( b = 60 \)
- \( c = 36 \)

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

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

Now, substituting the values:

\[
D = 60^2 - 4(25)(36)
\]
\[
D = 3600 - 3600
\]
\[
D = 0
\]

Since the discriminant \( D = 0 \), this means that the quadratic equation has exactly one real solution (also known as a repeated or double root).

Therefore, the number of real solutions to the equation \( 25x^2 + 60x + 36 = 0 \) is:

**1 real solution.**