Question

find quadratic polynomial whose zeroes are 7+√3 and 7-√3​

Answer 1

Answer:

${x}^{2} - 14x + 46$

Answer 2

Question :-

find quadratic polynomial whose zeroes are 7+√3 and 7-√3

Answer :-

x² - 14x + 46

Given :-

zeroes of the quadratic polynomial are 7+√3 and 7-√3​

To find :-

Quadratic polynomial

Solution :-

        Let the quadratic polynomial be p(x)

A quadratic polynomial is of the form

=>  k[ x² - (sum of zeroes)x + (product of zeroes) ]

Given zeroes,

and

★ Sum of zeroes = 7+√3 + 7-√3​

                            = 7 + 7

                            = 14

★ Product of roots = (7+√3)(7-√3)

                               = 7(7-√3) + √3(7-√3)

                               = 49 - 7√3 + 7√3 - √3²

                               = 49 - 3

                               = 46

   The quadratic polynomial is                              

         k[ x² - (14)x + 46 ]

         k[ x² - 14x + 46]

Put k = 1, ( or any number )

 

=> x² - 14x + 46