Question 1037105: form a polynomial f(x) with real coefficients having the given degree and zeros:
degree 5; zeros 7; -i; -7+i Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! factor of (x-5) is one.
factor (x^2+1) are two more
-7+i,-i -7-i ,-7+i are all factors
x^2+7x+c, which will give a root of (1/2)(-7+/- sqrt(49-4c)). I need to make this -14+/- sqrt(196-4(1)(50))
That will make the discriminant -4 and the square root +/-2i. Divide that by 2 and get i.
Therefore, the last quadratic factor is x^2+14x+50.
Their product is the function: x^5+7x^4-47x^3+343x^2-48x-350
