Question

The quadratic equation whose one rational root is 3 + √2 is (a) x² – 7x + 5 = 0 (b) x² + 7x + 6 = 0 (c) x² – 7x + 6 = 0 (d) x² – 6x + 7 = 0​

Answer 1

Answer:

(a) x²– 7x + 5 = 0

Step-by-step explanation:

one root is 3 + √2

one root is 3 + √2∴ other root is 3 – √2

one root is 3 + √2∴ other root is 3 – √2∴ Sum of roots = 3 + √2 + 3 – √2 = 6

one root is 3 + √2∴ other root is 3 – √2∴ Sum of roots = 3 + √2 + 3 – √2 = 6Product of roots = (3 + √2)(3 – √2) = (3)² – (√2)² = 9 – 2 = 7

one root is 3 + √2∴ other root is 3 – √2∴ Sum of roots = 3 + √2 + 3 – √2 = 6Product of roots = (3 + √2)(3 – √2) = (3)² – (√2)² = 9 – 2 = 7∴ Required quadratic equation is x² – 6x + 7 = 0