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write a quadratic equation whose roots are 5+i√2 & 5-i√2?
2 Answers
- 9 years agoFavorite Answer
Ans : If quadratic eq is of form aX^2 + bX + c = 0, so X^2 + b/a X + c/a = 0 then
Sum of roots = 10 = - b / a so b / a = 10
Product of roots = 25 + 2 = 27 = c / a
So quadratic eq is X^2 + 10 X + 27 = 0
- s kLv 79 years ago
If r is a root of f(x), then (x - r) is a factor of f(x). That is, if r1 and r2 are the only roots of f(x), then f(x) = a(x - r1)(x - r2), where a is any nonzero real number.
r1 = 5 + iâ2
r2 = 5 - iâ2
f(x) = a(x - 5 - iâ2)(x - 5 + iâ2)
f(x) = a(x^2 - 10x + 27)
