calculate the value of a when

Question

calculate the value of k when 2x³+4kx²-3k²x-2 divided by x-k gives a remainder of 10

Answer 1

After much blood, sweat and tears (and I may have gotten this wrong!), the long division for this is:

        2x^2 + 6kx+3k^2

        ---------------------------

x-k  / 2x^3+4kx^2-3k^2x-2

         2x^3-2kx^2

          --------------

                  6kx^2-3k^2x

                  6kx^2-6k^2x

                  ----------------

                            3k^2x-2

                            3k^2x-3k^3

                            ----------------

                                      3k^3-2=10

k^3=4

k is the cube root of 4.

 

Hope that helps,

Deanna

Answer 2

do long division and set remainder equal to 10. you should get k = cube root of 4

 

or

 

evaluate equation 2x³ + 4kx² - 3k²x - 2 = 10 when x = k

 

2k³ + 4k³ - 3k³ - 2 = 10

 

3k³ - 2 = 10

 

3k³ = 12

 

k³ = 4

 

k = ³√4   same answer