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JEE Main 20149 AprilOnline
Exam
JEE Main
Year
2014
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2014 · 9 April · Online · Mathematics · Quadratic Equation

If equations a x ^ 2 + bx + c = 0, (a, b, c ∈ R, a ≠ 0) and 2 x ^ 2...

If equations ax2+bx+c=0,(a,b,c∈R,a≠0)a{x}^{2} + bx + c = 0, \left(a, b, c \in R, a \ne 0\right) and 2x2+3x+4=02{x}^{2} + 3x + 4 = 0 have a common root, then a:b:ca: b: c equals :

Options

  1. A2:3:42: 3: 4
  2. B4:3:24: 3: 2
  3. C1:2:31: 2: 3
  4. D3:2:13: 2: 1

Correct answer

A. 2:3:42: 3: 4

Step-by-step solution

ax2+bx+c=0a{x}^{2} + bx + c = 0 ....(i)

2x2+3x+4=02{x}^{2} + 3x + 4 = 0 ....(ii)

For equation (ii), D=9−4(2)(4)=−23<0D = 9 - 4\left(2\right)\left(4\right) = - 23 < 0

Roots are complex conjugates.

⇒⇒ Both roots are common in equation (i) and (ii).

∴a2=b3=c4∴ \dfrac{\text{a}}{2} = \dfrac{\text{b}}{3} = \dfrac{\text{c}}{4}

⇒ a:b:c: :2:3:4\text{⇒ a}\text{:}\text{b}\text{:}\text{c}\text{: :}2\text{:}3\text{:}4
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