Question

Question
How many real solutions does the following quadratic equation have?

25x^2+60x+36=0


(1 point)
solution(s)
Remai

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 discriminant \( D \) is given by:

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

where \( a \), \( b \), and \( c \) are the coefficients of the quadratic equation \( ax^2 + bx + c = 0 \).

For the given equation:

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

Now, we can calculate the discriminant:

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

The value of the discriminant is \( 0 \).

According to the properties of quadratic equations:

- If \( D > 0 \), there are two distinct real solutions.
- If \( D = 0 \), there is exactly one real solution (a repeated root).
- If \( D < 0 \), there are no real solutions.

Since \( D = 0 \), the quadratic equation \( 25x^2 + 60x + 36 = 0 \) has **exactly one real solution**.