What is the condition that one root of the quadratic equation ax^2 + bx + c =0 is reciprocal of the other ?
What is the condition that one root of the quadratic equation ax2 + bx + c=0 is reciprocal of the other ?
A) a = b
B) b = c
C) a = c
D) a + b + c = 0
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2 Answers
Correct option is (C) a = c
Let \(\alpha\;and\;\frac1\alpha\) be roots of equation \(ax^2+bx+c=0.\)
\(\therefore\) Product of roots \(=\frac ca\)
\(\Rightarrow\frac ca=\alpha.\frac1\alpha=1\)
\(\Rightarrow\) c = a
Hence, the condition that one root of the quadratic equation \(ax^2+bx+c=0\) is reciprocal of the other is a = c.
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