Question

Find a quadratic polynomial one of whose zeroes is (3+√2) and the sum of its zeroes is 6.

Answer 1

Let α and β are the zeroes of a quadratic polynomial.

Given: one zero(α)= 3+√2
Sum of its zeroes (α+ β)= 6
(α+ β)= 6

3+√2 + β= 6
β = 6- (3+√2)= 6 -3 -√2= 3-√2
β= 3 -√2

Product of zeroes (α. β) = (3+√2) (3-√2)
α. β =( 3)² - (√2)²= 9 - 2= 7
[(a+b) (a-b)= a² - b²]
α. β = 7

Required Polynomial= k [x²-(Sum of zeroes)x +( Product of zeroes)]
= k[ x² -(α+ β)x +(α. β], where k is a non zero real number.

= x² -(6)x + (7) [ here k = 1]
= x² - 6x + 7

Hence, a quadratic polynomial is  x² - 6x + 7.
HOPE THIS WILL HELP YOU...

Answer 2

given :Sum of the zeroes 6         
           one of the zero is (3+√2)==αanother zero is 3-√2==β because 3+√2+β=6                                    β=6-3+√2                                   
                                    β=3-√2
So here in order to get the equation we need substitute in general formula of quadratic equationx²-(α+β)+αb
x²-(6)x+((3+√2)×(3-√2))    {(a+b)(a-b)==a²-b²}

x²-6x+(9-2)

x²-6x+(7)

x²-6x+7 is the answer.

Hope this helps u .