Aquadratic 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)

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