Question 1156241: Let P(x)=x4 −2x3 −10x2 +6x+45
▪ Use the Rational Zero Theorem to list all the possible rational zeros.
▪ Then find all zeros exactly (rational, irrational, and imaginary).
Hint: Use the Rational Zero Theorem, a graphing calculator, and synthetic division if needed.
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Since the leading coefficient is 1, the Remainder theorem provides this list of possible zeros
(all of them are divisors of the constant term 45, in this case)
+/-1, +/-3, +/-5, +/-9, +/-15, +/-45.
Next, the plot below
Plot y = 
shows the root x= 3 of the multiplicity at least 2.
So, I divide by  , and I get the quotient  .
This quotient is a quadratic polynomial with negative discriminant, so it has no real roots.
Therefore, factoring over real numbers is
=  .
You may go forward to find complex zeroes of the quadratic quotient.
|
|
|
