Question

How many real solutions does the following quadratic equation have? 25x2+60x+36=0

Answer 1

What’s the answer

Answer 2

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

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

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

In our case:
- \(a = 25\)
- \(b = 60\)
- \(c = 36\)

Now, we calculate the discriminant:

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

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

In quadratic equations, the number of real solutions is determined by the value of the discriminant:
- 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.

Answer 3

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