Write a quadratic equation whose roots are

Question

6+-2sqrt5.?

Answer 1

The roots of quadratic equation are 6 + 2√ 5 and 6 - 2√ 5

From factor theorem, when f(c) = 0 then x - c is a factor of polynomial.

f(x) = [x - (6 + 2√5)][x - (6 - 2√5)]

= [ x - 6 - 2√5][x - 6 + 2√5]

= [(x - 6) - 2√5][(x - 6) + 2√5]

= [(x - 6)² - (2√5)²]

= x² + 36 - 12x - 20

f(x) = x² - 12x + 16

Required quadratic equation is x² - 12x + 16.