Question

A quadratic equation is shown below: 3x2 − 15x − 10 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 4x2 − 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answer 1

Part A:

The radicand for the quadratic equation is called the discriminant. This can be calculated through the equation,
D = B² - 4AC
where D is the discriminant, A, B, C are the numerical coefficients of the terms.

Substituting the values to the equation,
D = (-15)² - (4)(3)(-10) = 345
Since the value of the discriminant is a positive value then the equation will have real roots and are distinct.

Part B:
From the equation,
4x² - 8x - 5 = 0

If the roots are a and b,
The sum of a and b should be equal to -B/A
a + b = -(-8)/4 = 2

The product should be equal to C/A.
ab = -20.

The value of a and b are 10 and -2.

The roots are there 10/4 = 5/2 and -2/4 = -1/2.

Roots: 5/2 and -1/2