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Question

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


A
0
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B
5
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C
16
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D
6
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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 = 5

Mathematics

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