SOLUTION: Find the polynomial of least degree having zeros; sqrt^7, -5, and 6

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Question 920961: Find the polynomial of least degree having zeros; sqrt^7, -5, and 6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given zeros:sqrt%287%29=2.65,+-5, and 6
find: the polynomial of least degree

use zero product formula
%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 substitute x%5B1%5D=sqrt%287%29,x%5B2%5D=-5, and x%5B3%5D=6
%28x-sqrt%287%29%29%28x%2B5%29%28x-6%29
%28x%5E2%2B5x-sqrt%287%29%2Ax-5sqrt%287%29%29%28x-6%29
x%5E3-sqrt%287%29x%5E2-x%5E2%2Bsqrt%287%29x-30x%2B30sqrt%287%29...or we can use sqrt%287%29=2.65 approximately
x%5E3-2.65x%5E2-x%5E2%2B2.65x-30x%2B30%2A2.65
x%5E3-3.65x%5E2-27.35x%2B79.5
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+90%2C+x%5E3-3.65x%5E2-27.35x%2B79.5%29+