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Question
Find the polynomial having roots at 3 , −5 , 7 , 6 and −2 .
Answer
The polynomial generated from the given zeros is: P(x)=x5−9x4−21x3+281x2−72x−1260
Explanation
Step 1: Turn the zeros into factors:
Zero | Factor |
3 | x−3 |
−5 | x+5 |
7 | x−7 |
6 | x−6 |
−2 | x+2 |
Step 2: Multiply the factors together:
P(x)=(x−3)⋅(x+5)⋅(x−7)⋅(x−6)⋅(x+2)=x5−9x4−21x3+281x2−72x−1260