Relations Between Roots Solution2





The page relations between roots solution2 is containing solution of some practice questions from the worksheet relationship between roots and coefficients.

(2) Form a quadratic equation whose roots are

(i)  3 , 4

Solution:

Here roots of the quadratic equation are 3 and 4.

α = 3      β = 4

General form of quadratic equation whose roots are α and β

 x² - (α + β) x + α β = 0

α + β = 3 + 4

        = 7

α β = 3 (4)

      = 12

by applying those values in the general form we get

 x² - (7) x + 12 = 0

Therefore the required quadratic equation is x² - 7x + 12 = 0


(ii) 3 + √7 , 3 - √7

Solution:

Here roots of the quadratic equation are 3 + √7 and 3 - √7.

α = 3 + √7      β = 3 - √7

General form of quadratic equation whose roots are α and β

 x² - (α + β) x + α β = 0

α + β = 3 + √7 + 3 - √7

        = 6

α β = (3 + √7)(3 - √7)

      = 3² - 7²

      = 9 - 49

      = -40

by applying those values in the general form we get

 x² - (6) x + (-40) = 0

Therefore the required quadratic equation is x² - 6x - 40 = 0


(iii) (4 + √7)/2 , (4 - √7)/2

Solution:

Here roots of the quadratic equation are (4 + √7)/2 and (4 - √7)/2.

α = (4 + √7)/2     β = (4 - √7)/2

General form of quadratic equation whose roots are α and β

 x² - (α + β) x + α β = 0

α + β = (4 + √7)/2 + (4 - √7)/2

        = (4 + √7 + 4 - √7)/2

        = 8/2

        = 4

α β = [(4 + √7)/2] [(4 - √7)/2]

      = (4² - (√7)²)/4

      = (16 - 49)/4

      = -33/4

by applying those values in the general form we get

 x² - 4 x + (-33/4) = 0

(4 x² - 16- 33)/4 = 0

4 x² - 16- 33 = 0

Therefore the required quadratic equation is 4 x² - 16- 33 = 0

These are the problems solved in the page relations between roots solution2.

relations between roots solution2