Question

construct a cubic equation with root (i) 1, 2 and 3 ,(ii) 1, 1 and -2 ,(iii) 2, 1/2 and 1​

Answer 1

Step-by-step explanation:

(i) Given roots are α = 1, β = 2, γ = 3 The cubic equation is x3 – x2 (α + β + γ) + x (αβ + βγ + γα) – αβγ = 0 ⇒ x3 – x2 (1 + 2 + 3) + x (2 + 6 + 3) – (1) (2) (3) = 0 ⇒ x3 – 6x2 + 11x – 6 = 0 (ii) α = 1, β = 1, γ = -2 The cubic equation is x3 – x2 (α + β + γ) + x (αβ + βγ + γα) – αβγ = 0 ⇒ x3 – x2 (1 + 1 – 2) + x (1 – 2 – 2) – (1) (1) (-2) = 0 ⇒ x3 – 0x2 – 3x + 2 = 0 ⇒ x3 – 3x + 2 = 0 (iii) α = 2, β = 1/2, γ = 1 The cubic equation is 2x3 – 7x2 + 7x – 2 = 0Read more on Sarthaks.com - https://www.sarthaks.com/868968/construct-a-cubic-equation-with-roots-i-1-2-and-3-ii-1-1-and-2-iii-2-1-2-and-1

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