Question

Construct a cubic equation with roots 2,1/2,1

Answer 1

Answer:

2x^3 - 7x^2 + 7x - 2 = 0

Step-by-step explanation:

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Answer 2

Given,

α = 2

β = 1/2

γ = 1

To find,

We have to find the cubic equation with the given roots.

Solution,

The required cubic equation is  2x³ - 7x² + 7x -2 =0.

We can simply find the cubic equation whose roots are given by the sum of roots, the sum of the products of the roots, and the products of the roots.

Cubic Equation = x³- x²(α + β + γ) + x (αβ + βγ + γα) – αβγ = 0

(α + β + γ)  = 2+1+1/2

                 = 7/2

(αβ + βγ + γα) = 2(1/2) + (1/2)1 + (1)2

                      = 1 + 1/2 + 2

                      = 7/2

αβγ  = 2* 1/2 *1

        = 1

Substituting the values of (α + β + γ), (αβ + βγ + γα), and  αβγ in the cubic equation, we get

           x³- 7/2x² + 7/2x -1

          2x³ - 7x² + 7x -2 =0

Hence, the required cubic equation is  2x³ - 7x² + 7x -2 =0