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

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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)   (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
--------------
Use the quadratic eqn to get the 2 roots.
------------
(-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
--------
To check:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=69 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -0.469337613708192, -2.13066238629181. Here's your graph:
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