SOLUTION: if x=square root 7 is aroot of x^3-3x^2-7x+21=0, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Question 597016: if x=square root 7 is aroot of x^3-3x^2-7x+21=0, use synthetic division to factor the polynomial completely and list all real solutions of the equation.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
if x=square root 7 is aroot of x^3-3x^2-7x+21=0, use synthetic division to factor the polynomial completely and list all real solutions of the equation.
**
..√7..|...1...-3....-7....21
..............√7...7-3√7.-21
..........1..-3+√7..-3√7..0
f(x)=(x-√7)(x^2+(-3+√7)x-3√7)
..
x^2+(-3+√7)x-3√7
solve by following quadratic formula:

a=1, b=(-3+√7), c=-3√7
x=3
or
x≈-√7
..
all real soltions: x=√7,-√7, and 3
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