Zeros of polynomial functions
Answers are for parents and teachers.
1
Which are polynomial functions, and what is the degree of each: 4x² − x, 7, x⁻² + 1, 2ˣ?
4x² − x: degree 2. 7: degree 0. x⁻² + 1 and 2ˣ are not polynomial functions.
2
Find the set of zeros of x² − 5x − 14.
(x − 7)(x + 2) = 0, so {−2, 7}.
3
Find the set of zeros of x³ + 3x² − 4x.
x(x² + 3x − 4) = x(x + 4)(x − 1) = 0, so {−4, 0, 1}.
4
−2 is a zero of f(x) = x² + bx − 8. Find b, the other zero, and f(5).
4 − 2b − 8 = 0, so b = −2. f(x) = (x − 4)(x + 2): other zero 4. f(5) = 25 − 10 − 8 = 7.
5
Find the set of zeros of 8x³ + 27.
8x³ + 27 = (2x + 3)(4x² − 6x + 9). The second factor has no real zero (4x² − 6x + 9 = (2x − 1.5)² + 6.75). So 2x + 3 = 0 and the set is {−3/2}.