Question
Consider the equation
4x^2 – 16x + 25 = 0.
(a) Show how to compute the discriminant, b^2 – 4ac, and then state whether there is one real-number solution, two different real-number solutions, or two different imaginary-number solutions.
(b) Use the quadratic formula to find the exact solutions of the equation. Show work. Simplify the final results as much as possible.
4x^2 – 16x + 25 = 0.
(a) Show how to compute the discriminant, b^2 – 4ac, and then state whether there is one real-number solution, two different real-number solutions, or two different imaginary-number solutions.
(b) Use the quadratic formula to find the exact solutions of the equation. Show work. Simplify the final results as much as possible.
Answers
Marth
(a) The equation is in the form ax^2 + bx + c
Use those values for b^2 - 4ac.
(-16)^2 - 4*4*25
= 256 - 400
= -144
The determinant is negative, so there will be two imaginary solutions.
(b) The quadratic equation is x = (-b +/- sqrt(determinant))/(2a)
Using the values of a, b, and c from the equation, we get
x = (16 +/- sqrt(-144))/(2*4)
x = (16 +/- 12i)/8
x = 2 +/- 3i/2
Use those values for b^2 - 4ac.
(-16)^2 - 4*4*25
= 256 - 400
= -144
The determinant is negative, so there will be two imaginary solutions.
(b) The quadratic equation is x = (-b +/- sqrt(determinant))/(2a)
Using the values of a, b, and c from the equation, we get
x = (16 +/- sqrt(-144))/(2*4)
x = (16 +/- 12i)/8
x = 2 +/- 3i/2
Pamela
Would this be an appropriate answer for b?
x= 4+3i/2, 4-3i/2
x= 4+3i/2, 4-3i/2
Marth
How did you get 4 +/- 3i/2?
Pamela
I figured 4*4 = 16. This is not right is it?
Marth
You divide by 8 at the end. 16/8 = 2