Question

determine the discriminant of the quadratic equation below. use the value of the discriminant to determine the nature of the solutions.

\\25q^2 - 40q + 16 = 0\\

the value of the discriminant is 0.

choose the nature of the solution.

a. one repeated real solution
b. two irrational solutions
c. two complex solutions that are not real
d. two rational solutions

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Identify Coefficients

Identify the coefficients \(a\), \(b\), and \(c\) from the standard form quadratic equation \(aq^2 + bq + c = 0\):

$$25q^2 - 40q + 16 = 0$$

$$a = 25, \quad b = -40, \quad c = 16$$

Step 2: Calculate the Discriminant

Substitute the coefficients into the discriminant formula \(D = b^2 - 4ac\):

$$D = (-40)^2 - 4(25)(16)$$

$$D = 1600 - 1600$$

$$D = 0$$

Step 3: Determine the Nature of the Solution

Since the discriminant is exactly \(0\), the quadratic equation has one repeated real solution (also known as one unique real root).

Answer:

The value of the discriminant is 0.

The nature of the solution is A. one repeated real solution.