Question

- Form a quadratic equation, when, one root = 3 + 2√5, sum of the roots = 9​

Answer 1

Step-by-step explanation:

Heya !!!

Let other zero be Beta .

Alpha = ( 3 - ✓5 )

Sum of zeroes = 6

Alpha + Beta = 6

3 - ✓5 + Beta = 6

Beta = ( 6 - 3 + ✓5 ) = ( 3 + ✓5 )

★ Product of zeroes = Alpha × Beta = ( 3 - ✓5 ) ( 3 + ✓5 ) = (3)² - (✓5)² = 9-5 = 4

Therefore,

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

=> X² - ( 6 )X +4

=> X² - 6X + 4 .

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