SOLUTION: What is the solution of 5 = 17x^2 - 200x ? A. 1 real number B. 2 complex numbers that are conjugates C. 2 real unequal numbers D. 0 E. none of these

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: What is the solution of 5 = 17x^2 - 200x ? A. 1 real number B. 2 complex numbers that are conjugates C. 2 real unequal numbers D. 0 E. none of these      Log On


   

Question 936694: What is the solution of 5 = 17x^2 - 200x ?
A. 1 real number
B. 2 complex numbers that are conjugates
C. 2 real unequal numbers
D. 0
E. none of these
Found 3 solutions by TimothyLamb, Alan3354, reviewermath:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
5 = 17x^2 - 200x
17x^2 - 200x - 5 = 0
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the above quadratic equation is in standard form, with a=17, b=-200 and c=-5
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
17 -200 -5
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 11.789653
x = -0.0249470996
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answer:
C. 2 real unequal numbers
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the solution of 5 = 17x^2 - 200x ?
17x%5E2+-+200x+-+5+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B-200x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-200%29%5E2-4%2A15%2A-5=40300.

Discriminant d=40300 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--200%2B-sqrt%28+40300+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-200%29%2Bsqrt%28+40300+%29%29%2F2%5C15+=+13.3582866332949
x%5B2%5D+=+%28-%28-200%29-sqrt%28+40300+%29%29%2F2%5C15+=+-0.0249532999615771

Quadratic expression 15x%5E2%2B-200x%2B-5 can be factored:
15x%5E2%2B-200x%2B-5+=+%28x-13.3582866332949%29%2A%28x--0.0249532999615771%29
Again, the answer is: 13.3582866332949, -0.0249532999615771. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-200%2Ax%2B-5+%29

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First, we need to compute the discriminant b^2-4ac: b^2-4ac = 40300.
Looks like C

Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
What is the solution of 5 = 17x^2 - 200x ?
A. 1 real number
B. 2 complex numbers that are conjugates
C. 2 real unequal numbers
D. 0
E. none of these
Solution:
Express the equation in the form ax%5E2+%2B+bx+%2B+c+=+0, then identify the values of a, b, and c.
17x%5E2+-+200x+-+5+=+0
a = 17, b = -200, and c = -5
The discriminant is b%5E2+-+4ac = 40340 > 0 [positive number]
Therefore, the answer is C. 2 real unequal numbers