Question 53181: The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
Possible solutions:
a.) f(x)=(x+3)(x^2+16)
b.) f(x)=(x+3)(x^2+8x+16)
c.) f(x)=(x+3)(x^2-8x+16)
d.) f(x)=(x-3)(x^2+16)
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
COEFFICIENTS ARE REAL.
HENCE IF 4i IS A OOT ,ITS CONJUGATE -4i SHOULD ALSO BE A ROOT .
HENCE THE 3 ROOTS ARE -3,4i,-4i..SINCE LEADIN COEFFICIENT IS ONE
F(X) = (X+3)(X-4i)(X+4i)=(X+3)(X^2+16)
A IS THE ANSWER
|
|
|
