Question

A quadratic equation is shown below: 4x2 − 12x + 9 = 0
Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)
Part B: Solve 9x2 − 30x + 25 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answer 1

A)

The discriminant (radicand) is √(b^2-4ac), let us call this "d" for the discriminant.

If:

d<0, there are no real solutions (though there are two imaginary ones)

d=0, there is one real solution

d>0, there are two real solutions.

In this case, d=12^2-4(4)9

d=144-144

d=0

So there is one real solution.

B)

9x^2-30x+25=0

9x^2-15x-15x+25=0

3x(3x-5)-5(3x-5)=0

(3x-5)(3x-5)=0

(3x-5)^2=0

x=5/3

x=1 2/3