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JEE Main 20137 April
Exam
JEE Main
Year
2013
Date
7 April
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2013 · 7 April · Mathematics · Quadratic Equation

If the equations x ^ 2 + 2 x + 3 = 0 and a x ^ 2 + bx + c = 0, a,...

If the equations x2+2x+3=0{x}^{2} + 2 x + 3 = 0 and ax2+bx+c=0,a{x}^{2} + bx + c = 0, a,b,c∈R,a, b, c \in R, have a common root, then a:b:ca: b: c is:

Options

  1. A1:3:21: 3: 2
  2. B3:1:23: 1: 2
  3. C1:2:31: 2: 3
  4. D3:2:13: 2: 1

Correct answer

C. 1:2:31: 2: 3

Step-by-step solution

As the roots of x2+2x+3=0{x}^{2} + 2 x + 3 = 0 are imaginary, hence both the roots are common with ax2+bx+c=0a{x}^{2} + bx + c = 0.

∴a1=b2=c3∴ \dfrac{a}{1} = \dfrac{b}{2} = \dfrac{c}{3}.
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