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DIRECTIONS for the question: Solve the following question and mark the best possible option.
If the roots of the equation y3 – cy2 + ay – b = 0 are in the ratio 4 : 2 : 5 and b = 1080, find the value of a
  • a)
    132
  • b)
    242
  • c)
    342
  • d)
    362
Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for the question: Solve the following question and mark th...
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DIRECTIONS for the question: Solve the following question and mark th...
Let the roots be 4k, 2k and 5k
Therefore, (y – 4k)(y – 2k)(y – 5k)
= y3 – y2(5k + 4k + 2k) + y(20k2 + 8k2 + 10k2 – 40k3)
= y3 – 11ky2 + 38k2y – 40k3
But the given equation is
y3 – cy2 + ay – b = 0
Therefore, b = 40k3 = 1080
⇒ k3 = 27 ⇒ k = 3
Therefore, a = 38k2 = 38(9) = 342
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