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Chrome File Edit View History Bookmarks people window Help ti x Section 4.5 a My Blackboard Content-BacMail c Secure https:/www.cheaa.com/auth?action loain Do Homework- Thomason Clayton Secure https://www.math lomework aspxhomeworkld-487179260&questionld-2;&flushed-false;&cld; 5052277 2018SU-MATH-1314-85400 85401 Thomason Clayton 6/21/18 Homework: Section 4.5 Score: 0 of 1 pt 4.5.26 Form a third-degree polynomial function with real coefficients such that -6+ iand -9 are zeros. 80116 (6 complete) ? Hw Score: 28.13%, 4.e E Question h Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your answer.) Enter your answer in the answer box and then click Check Answer All parts showing Clear All Satisfaction guaranteed

Explanation / Answer

Solution: here the given roots of polynomial are complex root and real roots. The real root is -9 and the complex root is -6 + i but we know that complex root occurs is the conjugate parts,

If -6+1 is the root of this function then -6-i will also be the root.

So, also, it is said that it has real coefficients.

Now we can easily calulate the third degreee polynomial, i.e.

[x-(-6+i)]*[x-(-6-i)]*[x-(-9)]

=> [x+6-i]*[x+6+i]*[x+9]

=> [(x+6)2-i2]*[x+9]

=> [(x2+12x+36)-(-1)]*[x+9]

=> [(x2+12x+36+1)]*[x+9]

=> [(x2+12x+37)]*[x+9]

=> [(x2+12x+37)]*[x+9]

=> x3+21x2+145x+333

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