Question

# If one root of $$\displaystyle 5x^{2}+13x+k=0$$ is reciprocal of the other then $$k=$$

A
0
B
5
C
16
D
6

Solution

## The correct option is C $$5$$$$\displaystyle 5x^{2}+13x+k=0\: \: \therefore a=5,b=3,c=k$$Let one root be $$\alpha$$$$\therefore$$ Other root will be $$\displaystyle \frac{1}{\alpha }$$$$\therefore$$ Product of roots = $$\displaystyle \frac{c}{a }$$  $$\displaystyle \Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k}{5}\Rightarrow 5\times 1=k$$ $$\therefore$$ k = 5Mathematics

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