Asked by katt
Find all the zeroes of the polynomial function f(x) = x^3-5x^2 +6x-30. If you use synthetic division, show all three lines of numbers.
plss help I asked my friends but they don't know either
homework question
plss help I asked my friends but they don't know either
homework question
Answers
Answered by
Steve
you can see the details for synthetic division here:
https://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php
just enter your coefficients and it will show the workings
https://www.mathportal.org/calculators/polynomials-solvers/synthetic-division-calculator.php
just enter your coefficients and it will show the workings
Answered by
Bosnian
For x³ - 5 x² + 6 x - 30 you can use factoring by grouping:
x³ - 5 x² + 6 x - 30 = ( x³ - 5 x² ) + ( 6 x - 30 ) =
x² ∙ ( x - 5 ) + 6 ∙ ( x - 5) = ( x - 5 ) ∙ x² + ( x - 5 ) ∙ 6 =
( x - 5 ) ∙ ( x² + 6 )
Now:
Find root of x - 5
x - 5 = 0
Add 5 to both sides
x - 5 + 5 = 0 + 5
x = 5
x₁ = 5
Find roots of x² + 6
x² + 6 = 0
Subtract 6 to both sides
x² + 6 - 6 = 0 - 6
x² = - 6
Take square rot of both sides
x = ± √ ( - 6 )
x = ± √ ( - 1 ∙ 6 )
x = ± √ ( - 1 ) ∙ √6
x = ± i ∙ √6
x₂ = i ∙ √6
x₃ = - i ∙ √6
The solutions are:
x = - i ∙ √6 , x = i ∙ √6 , x = 5
x³ - 5 x² + 6 x - 30 = ( x³ - 5 x² ) + ( 6 x - 30 ) =
x² ∙ ( x - 5 ) + 6 ∙ ( x - 5) = ( x - 5 ) ∙ x² + ( x - 5 ) ∙ 6 =
( x - 5 ) ∙ ( x² + 6 )
Now:
Find root of x - 5
x - 5 = 0
Add 5 to both sides
x - 5 + 5 = 0 + 5
x = 5
x₁ = 5
Find roots of x² + 6
x² + 6 = 0
Subtract 6 to both sides
x² + 6 - 6 = 0 - 6
x² = - 6
Take square rot of both sides
x = ± √ ( - 6 )
x = ± √ ( - 1 ∙ 6 )
x = ± √ ( - 1 ) ∙ √6
x = ± i ∙ √6
x₂ = i ∙ √6
x₃ = - i ∙ √6
The solutions are:
x = - i ∙ √6 , x = i ∙ √6 , x = 5
Answered by
Katt
I feel like im inputting the wrong things its a bit confusing sorry could you explain how to input
Answered by
Katt
Thank you
Answered by
Steve
huh? There is a box for each coefficient, and a small drop-down menu to choose + or -. Enter 3 for your degree, and just enter the numbers from your function.
If that's really too hard, then just google synthetic division examples and you will find lots of how-tos.
If that's really too hard, then just google synthetic division examples and you will find lots of how-tos.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.