5.7 / 5.8 Roots and Zeros
Objectives: I can find the zeros of a polynomial function. Given zeros, I can create a polynomial function.
1. The length of each side of a cube is x+4. What is the volume of the cube in cubic inches?
a. 3x+12
b.
c.
d.
2. Which coordinate pairs represent the zeros of the function
and then you can check by using your calculator. Show all work!
a.
b.
c.
d.
? Solve by factoring,
(-1,0), (1,0)
(-1,0), (2,0)
(-1,0), (2,0), (1,0)
(2,0)( ),(-1,0)
3. Given that p(-2)=0, p(1)=0, and p(4)=0, which expression could be p(x)?
[Hint: How do we write our r-value back as a divisor?]
a.
b.
c.
d.
4. Which pair of values could NOT be the roots of a quadratic polynomial?
a.
b.
c.
d.
6+10i and 6+10i
23 and 23
4+i and 4-i
2 and 4
5. Which statement about the zeros of a cubic polynomial is true?
a. There must be one complex zero, not just real zeros.
b. If 2 and -3 are zeros, the conjugates -2 and 3 must also be zeros.
c. If the cubic polynomial has 4 zeros, then it must have complex coefficients.
d. If the polynomial is a cubic, then it must have a maximum of 3 zeros.
6. Given that p(-4)=0, p(2)=0,and p(-1)=0, create a functions for p(x).
7. The length of each side of a cube is 2x+1. What is the volume of the cube in cubic inches?