Show that each polynomial function has a real zero as described i...

Question

Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5

no zero greater than 1

Accepted Answer

For the following polynomial function prove that it has no zero greater than two where a function is nine X to the fourth plus five, X to the third minus six, X squared minus 15 X plus eight. Now, to solve this, we will make use of the bounded this theorem, the states that if we have a function X minus C and we take our F of X and divide it by X minus C, we want to check our resulting division with synthetic division. If our resulting division has no negative terms, then we do not have a zero greater than C. So we have X minus C where C is two. So let's run a synthetic division with C equals two. You have 958868 to 15 and eight and we're dividing buy or zero X equals two. So you want to see if our evaluated expression as negative terms or not. Let's first bring down or not. Once we bring that down, we can multiply the result by two that gives us 18. We can now add our two numbers together five and 18 to get 23 multiplied by two gives us 46 we can add these two numbers together to get 40 multiplied by two will give us 80. Just adding these together, you get 65 65 multiplied by two. Gives us 1 30. Their final number being the remainder as 1 38. You know, here we have no negative terms. So by the synthetic division we received no negative terms, which means our answer is answer a meaning we have no zero, greater than two. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

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Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=6x^4+13x^3-11x^2-3x+5 no zero greater than 1