Equation From Roots Solution5

In this page equation from roots solution5 we are going to see solution for the worksheet framing quadratic equation from roots.

Find quadratic polynomials each with the given numbers as sum and product of its zeroes respectively.

(i) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 3

                                    α + β = 3

Product of zeroes = 1

                α β = 1

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² - 3 x + 1

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(ii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 2

                                    α + β = 2

Product of zeroes = 4

                α β = 4

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² - 2 x + 4

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(iii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 0

                                   α + β = 0

Product of zeroes = 4

                α β = 4

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² - 0 x + 4

                                                  = x² + 4

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(iv) Let α and β are the roots of a quadratic equation

Sum of the zeroes = √2

                                     α + β = √2

Product of zeroes = 1/5

               α β = 1/5

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² - √2 x + (1/5)

                                                  =   5x² - √2 x + 1

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(v) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 1/3

                                    α + β = 1/3

Product of zeroes = 1

                α β = 1

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² – (1/3) x + 1

                                                  =   3x² - x + 3

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(vi) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 1/2

                                    α + β = 1/2

Product of zeroes = -4

                α β = -4

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² – (1/2) x - 4

                                                  = 2 x² - x - 8

(vii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = 1/3

                                    α + β = 1/3

Product of zeroes  =  -1/3

                α β  = -1/3

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² – (1/3) x + (-1/3)

                                                  = 3 x² - x - 1

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(viii) Let α and β are the roots of a quadratic equation

Sum of the zeroes = √3

                                   α + β = √3

Product of zeroes = 2

                α β = 2

One of the such polynomial is p(x) = x² - (α + β) x + α β

                                                  = x² – √3 x + 2

equation from roots solution5 equation from roots solution5  equation from roots solution5

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