Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If on

1.	Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :(1) (–3, –1)(2) (1, 3) (3) (–1, 0) (4) (0, 1)
Answer» Answer is (3) (–1, 0) f(x) = a(x – 3) (x – α) f(2) = a(α – 2) f(–1) = 4a(1 + α) f(–1) + f(2) = 0 ⇒ a(α – 2 + 4 + 4α) = 0 a ≠ 0 ⇒ 5α = – 2 α = \(\frac{2}{5}\) = - 0.4 α ∈ (–1, 0)

Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :(1) (–3, –1)(2) (1, 3) (3) (–1, 0) (4) (0, 1)

Answer»

Answer is (3) (–1, 0)

f(x) = a(x – 3) (x – α)

f(2) = a(α – 2)

f(–1) = 4a(1 + α)

f(–1) + f(2) = 0 ⇒ a(α – 2 + 4 + 4α) = 0

a ≠ 0 ⇒ 5α = – 2

α = \(\frac{2}{5}\) = - 0.4

α ∈ (–1, 0)

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Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :(1) (–3, –1)(2) (1, 3) (3) (–1, 0) (4) (0, 1)

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