Question

How many real solutions does the following quadratic equation have? 25x2+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 standard form of a quadratic equation is \( ax^2 + bx + c = 0 \), where \( a = 25 \), \( b = 60 \), and \( c = 36 \).

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

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

Substituting the values of \( a \), \( b \), and \( c \):

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

The discriminant \( D = 0 \) indicates that the quadratic equation has exactly one real solution (a repeated root).

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