if the ratio of the roots of the equation x^2 -px+q =0 be 1:2, find the relation between p and q.
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f(x) = x²-px+q = 0
Let a and b be zeroes of f(x).
Given , a/b = 1/2 ⇒ b = 2a
Sum of roots = a+b =a+ 2a = 3a = -(-p) = p ⇒ a = p/3
Product of roots = ab =q ⇒ a . 2a = 2a² = 2(p/3)² = 2p/9 = q
Hence 2p = 9q .
Let a and b be zeroes of f(x).
Given , a/b = 1/2 ⇒ b = 2a
Sum of roots = a+b =a+ 2a = 3a = -(-p) = p ⇒ a = p/3
Product of roots = ab =q ⇒ a . 2a = 2a² = 2(p/3)² = 2p/9 = q
Hence 2p = 9q .
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