Question

Form a polynomial whose real zeros and degree are given. ​zeros: negative 2−2​,negative 1−1​,44​, 55​; ​ degree: 4 type a polynomial with integer coefficients and a leading coefficient of 1.

Answer 1

We write the polynomial in its factored form first.
We have then:
(x + 2) * (x + 1) * (x-4) * (x-5)
We now rewrite the polynomial:
(x ^ 2 + x + 2x + 1) * (x ^ 2-5x-4x + 20)
(x ^ 2 + 3x + 1) * (x ^ 2-9x + 20)
x ^ 4 - 9x ^ 3 + 20x ^ 2 + 3x ^ 3 - 27x ^ 2 + 60x + x ^ 2 - 9x + 20
We now add terms of the same degree:
x ^ 4 + (-9 + 3) x ^ 3 + (20-27 + 1) x ^ 2 + (60-9) x + (20)
x ^ 4 + (-6) x ^ 3 + (-6) x ^ 2 + (21) x + (20)
x ^ 4 - 6x ^ 3 - 6x ^ 2 + 21x + 20
Answer:
The polynomial sought is:
x ^ 4 - 6x ^ 3 - 6x ^ 2 + 21x + 20