Algebra 2 problems(probability+roots)?
I have a few problems to solve for homework.
1.Find the product and then classify this polynomial by degree and number of terms. (W(W-1)(3W+2)
2.There are 7 students in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?
3.Use the rational root theorem to list all Possible rational roots of the polynomial equation--- (X^3)-(2X^2)+(9X)+2=0. Do not find the actual roots.
4.Probability of 3 green lights in a series of 4 lights. Red and green are equally likely occurrences.
5. (9X^4)-(8X^2)-4=0. Find complex roots and number of real roots.
Comments
1. w(w-1)(3w+2)
= w(3w^2 +2w - 3w - 2)
= w(3w^2 -w -2)
= 3w^3 - w^2 - 2w
There are three terms, and the degree is three (this is the highest exponent on any one of the terms).
2. There are 7 different choices for first, and then there will only be 6 choices left for second place.
7*6 = 42
3. Since the coefficient of the leading coefficient is 1, the possible rational roots are just the positive and negative factors of the constant term.
You should be able to list them.
4. Since the probability is equally likely, then the probability of red is 1/2 and the probability of green is also 1/2.
(1/2)^3 (1/2) = (1/8)(1/2) = 1/16
5. 9x^4 - 8x^2 - 4 = 0
Let u = x^2, then u^2 = x^4
9u^2 - 8u - 4 = 0
Use the quadratic formula to solve.
Once you find the roots, remember that you need to set them equal to x^2 and solve for x.