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Question

If one root of the quadratic equation $$ax^2+bx+c=0$$ is the reciprocal of the other, then


A
b=c
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B
a=b
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C
ac=1
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D
a=c
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Solution

The correct option is D $$a = c$$
Given quadratic equation is $$ax^2+bx+c=0$$
Let $$\alpha$$ and $$\beta$$ be the roots of the equation.
It is given that $$\alpha=\dfrac{1}{\beta}$$
Now, $$\alpha\beta =\dfrac ca$$
$$\therefore \dfrac ca=1$$
Hence, $$c=a$$

Mathematics

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