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 wit
Algebra.Com
Question 62538: 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 stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
-----------------
If f(x) has real coefficients and 3+i is a root, then x=3-i is also a root.
---------
So, f(x)=(x-4)(x-(3+i))(x-(3-i))
f(x)=(x-4)((x-3)^2+1)
f(x)=(x-4)(x^2-6x+10)
Cheers,
Stan H.
RELATED QUESTIONS
I dont understand
"The degree three polynomial f(x) with real coefficients and leading (answered by stanbon)
The degree three polynomial f(x) with real coefficients and leading
coefficient 1, has 4 (answered by khwang)
The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4... (answered by solver91311)
the degree three polynomial f(X) with real coefficients and leading coefficient 1, has 4... (answered by ankor@dixie-net.com)
the degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 (answered by Edwin McCravy)
The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 (answered by stanbon)
THE DEGREE THREE POLYNOMIAL f(x) WITH REAL COEFFICIENTS AND LEADING COEFFICIENT 1, HAS -3 (answered by stanbon)
The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 (answered by stanbon)
The degree three polynomial f(x) with real coefficients and leading coefficient 1 has -3... (answered by stanbon)