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3 years ago

What are the possible rational zeros of f(x) = x4 + 6x3 – 3x2 + 17x – 15?

2 answers:

6 0

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

Below are the choices that can be found from other sources:

± 1, ± 3, ± 5, ± 15

± 1, ± , ± , ± 

± 1, ± 3, ± 6, ± 15, ± 17 

± 1, ± , ± , ± , ±

The answer is ± 1, ± 3, ± 5, ± 15

strojnjashka [21]3 years ago

6 0

Answer with explanation:

The given fourth degree polynomial is:

$f(x)=x^4+6 x^3-3 x^2+17 x-15$

By rational root theorem , the possible Zeroes of the polynomial are factors of 15 .

Factors of 15 are

$=\pm 1, \pm 3, \pm 5, \pm 15$

There are 8 possible Zeroes of the given Polynomial expression.

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BaLLatris [955]

Here , we are provided with a table which shows 5 consecutive terms of an arithmetic sequence . But before solving further , let's recall that ;

The n'th term of a Arithmetic Sequence let's say it be ${\sf T_n}$ is given by ;

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Now , here we are given with ;

${\quad \qquad \sf \blacktriangleright \blacktriangleright \blacktriangleright T_{1}=8 \: and \: T_{5}=-4}$

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Now , by using the above formula , 5th term can be written as ;

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Putting the values and transposing 1st term to RHS , we have ;

${: \implies \quad \sf 4d = -4-8}$

${: \implies \quad \sf d=-\dfrac{12}{4}}$

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Now , as we got the common difference , so we can find out the missing terms now ;

${: \implies \quad \sf T_{2}= T_{1}+(2-1)d}$

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${: \implies \quad \bf \therefore \: T_{2}= 5}$

Now

${: \implies \quad \sf T_{3}= T_{1}+(3-1)d}$

${: \implies \quad \sf T_{3}= 8 +2d}$

${: \implies \quad \sf T_{3}= 8-6}$

${: \implies \quad \bf \therefore \: T_{3}= 2}$

Also ,

${: \implies \quad \sf T_{4}= T_{1}+(4-1)d}$

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${: \implies \quad \sf T_{4}= 8-9}$

${: \implies \quad \bf \therefore \: T_{4}= -1}$

Now , The given table can be written as ;

${\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \bf n & \sf 1 & 2 & 3 & 4 & 5 \\ \cline{1-6} \bf T_{n} & \sf 8 & 5 & 2 & -1 & -4 \end{array}}$

Note :- Kindly view the answer from web , if you're not able to see the full answer from here ;

brainly.com/question/26750175

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3 years ago

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