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
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
5 answers
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
I feel like im inputting the wrong things its a bit confusing sorry could you explain how to input
Thank you
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.
2 answers