If one root of the equation \(\frac{x^2}{a}+\frac{1}{b}+\frac{1}{c}=0\

1.	If one root of the equation \(\frac{x^2}{a}+\frac{1}{b}+\frac{1}{c}=0\) = 0 is reciprocal of the other, then which of the following is correct ?(a) a = b (b) b = c (c) ac = 1 (d) a = c
Answer» (d) a = c The equation can be written as \(\frac{1}{a}x^2+\frac{1}{b}x+\frac{1}{c}=0\) i.e., bcx² + acx + ab = 0. Let a, \(\frac{1}{α}\) be the roots of the given equation, then product of roots = α x \(\frac{1}{α}\) = \(\frac{ab}{bc}\) ⇒ \(\frac{ab}{bc}\) = 1 ⇒ a = c.

If one root of the equation \(\frac{x^2}{a}+\frac{1}{b}+\frac{1}{c}=0\) = 0 is reciprocal of the other, then which of the following is correct ?(a) a = b (b) b = c (c) ac = 1 (d) a = c

Answer»

(d) a = c

The equation can be written as \(\frac{1}{a}x^2+\frac{1}{b}x+\frac{1}{c}=0\)

i.e., bcx² + acx + ab = 0.

Let a, \(\frac{1}{α}\) be the roots of the given equation, then

product of roots = α x \(\frac{1}{α}\) = \(\frac{ab}{bc}\) ⇒ \(\frac{ab}{bc}\) = 1 ⇒ a = c.