MAT1511/101/0/2024
Tutorial letter 101/0/2024
ASSESSMENT 01
PRECALCULUS MATHEMATICS B
MAT1511
Year module
IMPORTANT INFORMATION:
Please activate
my Unisa and myLife e-mail
account and
Department
ofyour
Mathematical
Sciences
make sure that you have regular access to the my Unisa module
website MAT1511-24-Y1, as well as your group website.
Note: This is a fully online module. It is therefore, only available on my Unisa.
Define tomorrow.
university
of south africa
QUESTION 1
1.1 P (x) = −x3 + 7x + 6
(a) Use the Factor Theorem, or otherwise, to show that x + 2 is a factor of P (x) .
(2)
(b) Solve P (x) = 0 by first factorising P (x) completely.
(3)
1.2 P (x) = 2x5 + 3x3 + 4x2 − 8
(a) List all possible rational zeros of P(x) given by the Rational Zeros Theorem. ($heck
to see which actually are zeros.)
(2)
(b) Show that 1 and −2 are the upper bound and lower bound, respectively, for the real zeros of
P (x) .
(3)
[10]
QUESTION 2
2.1 Use Descartes’ Rule of Signs to describe all possibilities for the number of positive, negative and
imaginary zeros of P (x) , where
P (x) = 4x3 − 3x2 − 7x + 9.
(You may summarise your answer in the form of a table.)
2.2 Find a polynomial, P (x) , with integer coefficients, that has 3, 0 and i as zeros.
(5)
(5)
[10]
QUESTION 3
3.1 Write
(2 + i)2 (3 − i)
2 − 3i
in the form a + bi, where a, b ∈ R.
(5)
3.2 Decompose
x3 − x + 2
x3 − 1
into partial fractions.
(10)
[15]