# if x=-1-3i is a root of f(x)=x^3+4x^2+14x+20, find all the other roots ( real and imaginary)?

• if x=-1-3i is a root of f(x)=x^3+4x^2+14x+20, find all the other roots ( real and imaginary)?

Answer #1 | 06/02 2014 19:47
f(x) = x³ + 4x² + 14x + 20 f(x) = (x + 2)(x² + 2x + 10) If the product of two factors equals zero, then one or both factors equal zero. If x + 2 = 0, x = - 2 If x² + 2x + 10 = 0, x² + 2x = - 10 x² + 2x + 1 = 1 - 10 (x + 1)² = - 9 x + 1 = √(- 9) x + 1 = √9 √(- 1) x + 1 = ± 3 i x = - 1 ± 3 i Other Root = - 1 + 3 i ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Positive: 62 %

Polynomials of the 2nd degree. ... f(x) = x 2 −2x −3. Find the roots of f(x), ... A double root. f(x) = x 2 −10x + 25. Find the roots of f(x), ...
Positive: 62 %
SOLUTION: Find the polynomial f(x) ... Find all roots of the polynomial x^3-x^2 ... If the coefficients are Real and 3+i is a root, 3-1 must be a root. f ...
Positive: 57 %
x +1. Using Maple 8, the roots of f are all complex. ... real root. Let f (x) = x5 +2x +9. ... (x) = 20x3 −2. Thus, f (0)