Question

Find a quadratic polynomial whose zeroes are 3+root 5 ÷5 and 3-root 5÷5

Answer 1

Answer:

25x² - 30x + 4 = 0

Step-by-step explanation:

Alpha = 3 + ✓5 / 5 and Beta = 3 - ✓5/5

Sum of zeroes = 3 + ✓5/5 + 3 - ✓5/5

=> 3 + ✓5 + 3 - ✓5/5

=> 6 /5

And,

Product of zeroes = ( 3 + ✓5/5 × 3 - ✓5/5)

=> ( 3 + ✓5 ) ( 3 - ✓5) / 25

=> ( 3)² - (✓5)²/25

=> 9 - 5/25 = 4 /25

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

=> X² - (6/5)X + ( 4/25)

=> X² -6X/5 + 4/25

=> 25X² - 30X + 4 = 0