Question

find the quadratic polynomial with zeroes 3+root2 and 3-root2

Answer 1

Heya !!!

Let Alpha = 3+✓2 and Beta = 3-✓2

Sum of zeroes = (Alpha + Beta) = 3+✓2 + 3 -✓2 = 6

And,

Product of zeroes = Alpha × Beta = (3+✓2)(2-✓2) = (3)² - (✓2)² = 9-2 = 7

Therefore,

Required Quadratic polynomial = X²-(Sum of zeroes)X + Product of zeroes

=> X²-(6)X + 7

=> X²-6X+7



HOPE IT WILL HELP YOU...... :-)

Answer 2

Heya Dear,

                      ______________________

Given , 

Zeroes of a quadratic polynomial is ( 3 + √2 ) and ( 3 - √2 ).

Sum of zeroes = 3 + √2 + 3 - √2 = 6

Product of zeroes = ( 3 + √2 ) ( 3 - √2 )

                             = (3)² - (√2)²

                             = 9 - 2

                             = 7.

The general form of a quadratic equation is :

= x² - ( sum of zeroes ) x + Product of zeroes

= x² - ( 6 )x + 7

= x² - 6x + 7.

The required quadratic polynomial is x² - 6x + 7.


Hope it helps !