How do you find a polynomial function that has zeros x=−5,1,2 and degree n=4?
A function f: R → R defined as f(x)=anxn + an-1xn-1 + ... + a2x2 + a1x + a0 is called a polynomial function in variable x.
Answer: f(x)=(x+5)2(x−1)(x−2) = x4 + 7x3 − 3x2 − 55x + 50
Let us look at step by step solution below.
A polynomial function f(x) with zeros x= -5, x=1, and x=2 has variables (x+5), (x -1), and (x-2).
It would be cubic if these were the only variables.
The query does not specify if the numbers -5, 1, and 2 are the only zeros. If this is the case, one of them must have multiplicity 2.
In either case, the following quartic will be appropriate:
⇒ f(x) = (x+5)2(x−1)(x−2)
⇒ (x2 + 25 + 10x) (x−1)(x−2)
⇒ x4 - 3x3 + 27x2 - 75x + 50 + 10x3 - 30x2 + 20x
⇒ x4 + 7x3 − 3x2 − 55x + 50