Question

find a quadratic polynomial, such that the product of 0 is 7 and one zero is 3 +root 2​

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...