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Find the value of $k$ for which the roots of the equation $3x^{2}–10+k=0$ are reciprocal of each other.
Given: The equation $3x^{2}– 10+k=0$
To do: To Find the value of k for which the roots of the equation are reciprocal of each other.
Solution:
Given equation:$3x^{2}-10x+k=0$
On comparing it to $ax^{2}+bx+c=0$,
we have, $a=3,\ b=-10,\ c=k$
Let $\alpha$ and $\frac{1}{\alpha}$ are the roots of the given quadratic equation.
product of the roots $=\frac{c}{a}$
$\alpha.\frac{1}{\alpha}=\frac{k}{3}$
$\Rightarrow\frac{k}{3}=1$
$\Rightarrow k=3$
Hence for $k=3$, the given equation will have roots reciprocal to each other.
Updated on: 10-Oct-2022
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