MAT1511 ASSIGNMENT 1 2023

MAT1511
ASSIGNMENT 1
2023

, QUESTION 1




Solution:



i).



P(x) = x 4 + x 3 + x 2 + x + 12



Number of sign changes = 0




𝐏𝐨𝐬𝐢𝐭𝐢𝐯𝐞 𝐍𝐞𝐠𝐚𝐭𝐢𝐯𝐞 𝐈𝐦𝐚𝐠𝐢𝐧𝐚𝐫𝐲 𝐓𝐨𝐭𝐚𝐥

0 4 0 4
0 2 2 4
0 0 4 4




ii).



P(x) = 2x 5 + x 4 + x 3 − 4x 2 − x − 3



Number of sign changes = 1




𝐏𝐨𝐬𝐢𝐭𝐢𝐯𝐞 𝐍𝐞𝐠𝐚𝐭𝐢𝐯𝐞 𝐈𝐦𝐚𝐠𝐢𝐧𝐚𝐫𝐲 𝐓𝐨𝐭𝐚𝐥

1 4 0 5
1 2 2 5
1 0 4 5