Question

If ∝ and 1/∝ are the zeros of the polynomial 3x²+x+(k-2) find K

Answer 1

∝ × 1 / ∝ = c / a

1 = k - 2 / 3

k - 2 = 3

k = 3 + 2

k = 5

•°• The value of k is 5

Answer 2

Sol: α and β are the zeroes of the polynomial f(x) = 2x² + 5x + k. Sum of the zeroes = α + β = -(coefficient of x) / (coefficient of x2) = -5/2. Product of the zeroes = αβ = -(constant term) / (coefficient of x2) = k/2. α²+β²+αβ = 21/4 ⇒ (α + β)2 - αβ = 21/4 ⇒ (-5/2)2 - k/2 = 21/4 ⇒ 25/4 - k/2 = 21/4 ⇒ k/2 = 25/4 - 21/4 ⇒ k/2 = 1 ⇒ k = 2.

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