Question

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b. Find the cubic polynomial if the sum, sum of the zeroes taken two at a
time and the product of its zeroes are 572.-7.-4 respectively.
(2x - 5x? - 14x+8 (i) 2x3 + 5x + 14x + 8
(ii) 2x + 5x? - 14x-8 (iv) 2x3 - 5x2 - 14x -8.​

Answer 1

Answer:

We know that the general form of a cubic polynomial is ax3 + bx2 + cx + d and the zeroes are α, β, and γ.

Let's look at the relation between sum, and product of its zeroes and coefficients of the polynomial.

α + β + γ = - b / a

αβ + βγ + γα = c / a

α x β x γ = - d / a

Let the polynomial be ax3 + bx2 + cx + d and the zeroes are α, β, γ

We know that,

α + β + γ = 2/1 = - b / a

αβ + βγ + γα = - 7/1 = c / a

α.β.γ = - 14/1 = - d / a

Thus, by comparing the coefficients we get, a = 1, then b = - 2, c = - 7 and d = 14

Now, substitute the values of a, b, c, and d in the cubic polynomial ax3 + bx2 + cx + d.

Hence the polynomial is x3 - 2x2 - 7x + 14.

Step-by-step explanation: