SOLUTION: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a product of linear and quadratic polynomials       Log On


   

Question 7732: The degree three polynomial f(x) with real coefficients and leading
coefficient 1, has 4 and 3 + i among its roots. Express f(x) as a
product of linear and quadratic polynomials with real coefficients.
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
4 and 3 + i among its roots
Another complex root must be the conjugate of 3+i, ie 3-i.
The corresponding quadratic monic equation is x^2 -6 x + 10 = 0 (why?)
[Hint: in one step sum and product of 3+i & 3-i]
Hence, f(x) = (x-4)(x^2 -6 x + 10)

Kenny