Question

A quadratic equation is shown below: 2x2 − 10x − 8 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 4x2 − 12x + 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 given quadratic equation is 2x²-10x-8=0

The radicand is given by b²-4ac where a, b, and c are the constants in a quadratic form ax²+bx+c

From the given equation, we have
a = 2
b = -10
c = -8

Radicand b²-4ac = (-10)² - 4(2)(-8) = 100 + 64 = 164

The radicand is >0 hence the quadratic equation has two distinct roots

PART B:

4x²-12x+5 = 0

We can use the factorization method to solve the equation
Firstly, we multiply 4 by 5 to get 20
Then we find the pair of numbers that multiply gives 20 and sum gives -12

The pair of number is -2 and -10
Rewriting the equation 
4x²-2x-10x+5 = 0
2x(2x-1)-5(2x-1) = 0
(2x-1)(2x-5) = 0

2x-1 = 0 and 2x-5 = 0
x = 1/2 and x = 5/2