How many real solutions does the following quadratic equation have?

Question

25x2+60x+36=0

(1 point)
solution(s)

Answer 1

To determine the number of real solutions of the quadratic equation $25x^2+60x+36=0$, we can use the discriminant method. The discriminant $\mathrm{\Delta }$ for a quadratic equation of the form $a{x}^2+bx+c=0$ is given by the formula:

$$\mathrm{\Delta }=b^2-4ac$$

In this case, the coefficients are:

• $a=25$
• $b=60$
• $c=36$

Now, we can calculate the discriminant:

$$\mathrm{\Delta }={60}^2-4\cdot 25\cdot 36$$

Calculating ${60}^2$:

$${60}^2=3600$$

Next, calculating $4\cdot 25\cdot 36$:

$$4\cdot 25=100$$

$$100\cdot 36=3600$$

Now, substituting back into the discriminant:

$$\mathrm{\Delta }=3600-3600=0$$

Since the discriminant $\mathrm{\Delta }$ is equal to 0, the quadratic equation has exactly one real solution (a double root).

Therefore, the answer is:

1 real solution.