MAT1511 Assignment 1 (ANSWERS) Semester 1 - 2023.
Questions asked: 1. Use Descartes’ Rule of Signs to determine the possible number of positive, negative and
imaginary zeros of P (x).
(i) P (x) = x
4 +x
3 +x
2 +x +12. (4)
(ii) P (x) = 2x
5 +x
4 +x
3 −4x
2 −x −3. (4)
2. Let P ...
,1 ADDENDUM A: YEAR ASSIGNMENT 01 3.2 – 3.5, 8.1, 8.3, 8.4 FIXED CLOSING DATE: 18 May 2023
UNIQUE NUMBER: 768575 NO EXTENSION CAN BE GRANTED 1. Use Descartes’ Rule of Signs to
determine the possible number of positive, negative and imaginary zeros of P (x). (i) P (x) = x 4 +x 3 +x 2
+x +12. (4) (ii) P (x) = 2x 5 +x 4 +x 3 −4x 2 −x −3. (4)
(i) To use Descartes' Rule of Signs to determine the possible number of positive, negative, and
imaginary zeros of P(x) = x^4 + x^3 + x^2 + x + 12, we need to count the sign changes in the coefficients
of the polynomial.
According to Descartes' Rule of Signs, the number of positive zeros of P(x) is either equal to the number of sign
changes or less than it by an even number. In this case, there are 1 sign change in the coefficients, so P(x) has
either 1 positive zero or 3 positive zeros (less by an even number).
To determine the number of negative zeros, we substitute -x for x in P(x) and count the sign changes:
According to Descartes' Rule of Signs, the number of negative zeros of P(x) is either equal to the number of
sign changes or less than it by an even number. In this case, there are 3 sign changes in the coefficients, so
P(x) has either 3 negative zeros or 1 negative zero (less by an even number).
Since the number of positive zeros and negative zeros can differ by an even number, the possible combinations
for the number of positive, negative, and imaginary zeros are:
- 1 positive zero and 3 negative zeros (or vice versa).
- 3 positive zeros and 1 negative zero (or vice versa).
- 1 positive zero, 1 negative zero, and 2 imaginary zeros.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller itsbesttutors. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.87. You're not tied to anything after your purchase.
