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The quadritic equations x2 –  6x  + a = 0 and x2 – cx + 6 = 0 have one root in common.  The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is [2009]
  • a)
    1
  • b)
    4
  • c)
    3
  • d)
    2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The quadritic equations x2 – 6x + a = 0 and x2 – cx + 6 = ...
Let the roots of equation x2 – 6x + α = 0 be α and 4 β and that of the equation
x2 –cx + 6 = 0  be α and 3β .
Then α + 4β = 6 ; 4aβ = α and α + 3β = c ; 3αβ = 6
⇒ α = 8
∴ The equation becomes  x2 – 6x + 8 = 0
⇒ (x –2) (x – 4) = 0
⇒ roots are 2 and 4 ⇒ α = 2, β = 1
∴ Common root is 2.
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The quadritic equations x2 – 6x + a = 0 and x2 – cx + 6 = ...
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The quadritic equations x2 – 6x + a = 0 and x2 – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is [2009]a)1b)4c)3d)2Correct answer is option 'D'. Can you explain this answer?
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