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Distance Formula

If x2+mx+1=...

Question

If $x^{2} + m x + 1 = 0$ and $(a - b) x^{2} + (b - c) x + (c - a) = 0$ have both roots common then which of the following is true?

A

m = - 1

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B

m = 2

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C

m = - 2

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D

b, a, c are in AP

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Solution

The correct options are
B $m = 2$
D b, a, c are in AP
$x^{2} + m x + 1 = 0$
$(a - b) x^{2} + (b - c) x + (c - a) = 0$
$c - a = a - b$
$∴ b, a, c$ are in A.P. b. b+d, b+2d
$m = \frac{c - b}{a - b} = \frac{b + 2 d - b}{b + d - b} = + 2$
$m = + 2$

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