If one of the zeroes of the polynomial $3x^2+8x+k$ is the reciprocal of the other, then what is the value of $k$?

Given: If one of the zeroes of the polynomial $3x^2+8x+k$ is the reciprocal of the other.

To do: To find the value of $k$.

Solution: 

Let $x$ and $\frac{1}{x}$ be the zeroes of the polynomial $3x^2+8x+k$.

Product of the polynomial$=x.\frac{1}{x}=\frac{k}{3}$

$\Rightarrow 1=\frac{k}{3}$

$\Rightarrow k=3$

Thus, $k=3$.

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Updated on: 10-Oct-2022

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