SOLUTION: IF ONE ROOT OF THE POLYNOMIAL 5x^2+13x+k IS THE RECIPROCAL OF THE OTHER,THEN WHAT IS THE VALUE OF K I WILL BE THANKFUL PRIYAL

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: IF ONE ROOT OF THE POLYNOMIAL 5x^2+13x+k IS THE RECIPROCAL OF THE OTHER,THEN WHAT IS THE VALUE OF K I WILL BE THANKFUL PRIYAL      Log On


   

Question 201668: IF ONE ROOT OF THE POLYNOMIAL
5x^2+13x+k
IS THE RECIPROCAL OF THE OTHER,THEN WHAT IS THE VALUE OF K
I WILL BE THANKFUL
PRIYAL
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
IF ONE ROOT OF THE POLYNOMIAL
5x^2+13x+k
IS THE RECIPROCAL OF THE OTHER,THEN WHAT IS THE VALUE OF K
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Use the quadratic eqn to get the 2 roots.
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(-13 + sqrt(169-20k))/10 = 10/(-13 - sqrt(169-20k))
(-13 + sqrt(169-20k))*(-13 - sqrt(169-20k)) = 100
169 - (169-20k) = 100
20k = 100
k = 5
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To check:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B13x%2B5+=+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=%2813%29%5E2-4%2A5%2A5=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+69+%29%29%2F2%5C5+=+-0.469337613708192
x%5B2%5D+=+%28-%2813%29-sqrt%28+69+%29%29%2F2%5C5+=+-2.13066238629181

Quadratic expression 5x%5E2%2B13x%2B5 can be factored:
5x%5E2%2B13x%2B5+=+%28x--0.469337613708192%29%2A%28x--2.13066238629181%29
Again, the answer is: -0.469337613708192, -2.13066238629181. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B13%2Ax%2B5+%29