Question

How many real solutions does the following quadratic equation have?

25x2+60x+36=0


(1 point)
solution(s)

Answer 1

To determine how many real solutions the quadratic equation \( 25x^2 + 60x + 36 = 0 \) has, we can use the discriminant, which is given by the formula:

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

For the given equation, we have:

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

Now, we can calculate the discriminant:

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

Calculating \( 60^2 \):

\[
60^2 = 3600
\]

Calculating \( 4 \cdot 25 \cdot 36 \):

\[
4 \cdot 25 = 100
\]
\[
100 \cdot 36 = 3600
\]

Now substituting back into the discriminant:

\[
D = 3600 - 3600 = 0
\]

The discriminant \( D = 0 \) indicates that there is exactly one real solution (also known as a repeated or double root).

Therefore, the quadratic equation \( 25x^2 + 60x + 36 = 0 \) has **1 real solution**.