Question

Use the discriminant to identify how many, and what kind of,

solutions the quadratic equation has. (Do not solve.) 25x²–20x + 4 = 0

Answer 1

The discriminant for the given quadratic equation is 0, indicating that there is one double root.

Step-by-step explanation:

The given equation 25x²–20x + 4 = 0 is a quadratic equation, where the coefficients are a = 25, b = -20, and c = 4. To determine the number and type of solutions, we can use the discriminant, which is given by

Discriminant (D) = b² - 4ac.

Substituting the values, we get

D = (-20)² - 4(25)(4) = 400 - 400 = 0.

Since the discriminant is equal to 0, there is only one solution to the quadratic equation. This type of solution is called a double root, where the parabola represented by the equation touches the x-axis at a single point.

Answer 2

The quadratic equation 25x²–20x + 4 = 0 has one real solution because its discriminant, calculated using the formula Δ = b² - 4ac, is zero, indicating a repeated or double root.

Step-by-step explanation:

To determine the number and kind of solutions of the quadratic equation 25x²–20x + 4 = 0, we use the discriminant, which is part of the quadratic formula. The formula to find the discriminant (Δ) is Δ = b² - 4ac, where a, b, and c are coefficients from the equation ax²+bx+c = 0.

For this equation, a = 25, b = -20, and c = 4. Plugging these values into the discriminant formula gives us:

Δ = (-20)² - 4(25)(4)

Δ = 400 - 400

Δ = 0

Since the discriminant is zero, this means that the quadratic equation has one real solution, and this solution is a repeated or double root. Thus, the quadratic equation will touch the x-axis at one point when graphed.