Asked by Pamela
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
Answered by
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
Answered by
Pamela
Would this be an appropriate answer for b?
x= 4+3i/2, 4-3i/2
x= 4+3i/2, 4-3i/2
Answered by
Marth
How did you get 4 +/- 3i/2?
Answered by
Pamela
I figured 4*4 = 16. This is not right is it?
Answered by
Marth
You divide by 8 at the end. 16/8 = 2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.