# Need to find c in a quadratic equation

1. Jun 11, 2012

### chomsky

1. The problem statement, all variables and given/known data

If α and $\frac{1}{αα}$are the roots of the equation $5x^{2}+13x+k$ then k will be:

a) 5
b) -5
c) 13
d) 1

2. Relevant equations

3. The attempt at a solution

I've tried multiplying both the roots to get $\frac{c}{a}$ and adding the roots to get $\frac{-b}{a}\frac{}{}$, and then I've tried to add the sum and the product of the roots on the LHS and corresponding to it, $\frac{c}{a}$ and $\frac{-b}{a}$ on the RHS. But I just can't get the answer, and I can't figure out how to solve this any differently. Any help or ideas on how to go about solving this type of question would be greatly appreciated.

2. Jun 11, 2012

### Infinitum

Hi chomsky!

Is the second root $1/\alpha$ or $1/\alpha^2$?

If it is the the first, the question would be really simple, as their product is

$$\alpha \cdot \frac{1}{\alpha} = \frac{k}{5}$$
What does this give you?

If the second, you won't get an answer matching your options. But you can use the relation from product of roots and substitute it in the equation from sum of roots to get a cubic equation in k.