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2015-09-30T21:44:37+05:30

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The given polynomial = ax² + bx + c
given that one root is double the other.
Let one root is m.
other root = 2m

sum of roots = -b/a
⇒ 2m+m = -b/a
⇒3m = -b/a
⇒ m = -b/3a ------------------------------(1)

product of roots = c/a
⇒ 2m×m = c/a
⇒ 2m² = c/a
⇒ m² = c/2a
Putting value of m from equation(1)
⇒(-b/3a)² = c/2a
⇒ b²/9a² = c/2a
⇒ b²/9a = c/2
⇒ 2b² = 9ac
2b² - 9ac = 0

So the condition is 2b² - 9ac = 0.
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