Question

Find a cubic polynomial with the sum, sum of the products of its zero taken two at a time and product of its zeros as 4, 1, -6 respectively.

Answer 1

Answer:

Step-by-step explanation:

Cubic polynomial : $x^{3}$ - (α+β+∅)x +(αβ+β∅+∅α)$x^{2}$-αβ∅ ----- eq 1

Given :

             (α+β+∅) = 4    -------- eq 2    (Sum Of zeroes)

       (αβ+β∅+∅α) = 1  ---------- eq 3    (Sum of product of zeroes)

             αβ∅       = -6 ----------eq 4    (Product of zeroes)

Sub eq 2, 3 and 4 in eq 1;

$x^{3}$ - 4x + $x^{2}$ - (-6) =  $x^{3}$ -4x + $x^{2}$ +6

$x^{3}$+ $x^{2}$ -4x   + 6 is the required polynomial

(For a cubic polynomial ax³ + bx² + cx + d, the zeroes are α, β and γ, where

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = - d/a              )

Hope this helps....

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