Polynomials (1 Viewer)

[taggs-sasuke]

Can someone please help me with the following Polynomials questions? Thank you very much!

Q1

If x^(3) +2x^(2)y - xy^(2) - 2y^(3) and x^(3) -7xy^(2) - 6y^(3) have (x+2y) as a factor, simplify:

x^(3) +2x^(2)y - xy^(2) - 2y^(3)
__________________________
x^(3) -7xy^(2) - 6y^(3)

A1

x - y
_____
x - 3y

Q2

Solve the equation x^(3) - 12x^(2) +39x - 28 = 0 if the roots are in arithmetic progression.

A2

x = 1, 4, 7

 

[tommykins]

q2 -

let roots be @-d, @, @+d then use sum/product of roots

 

[Trebla]

Can someone please help me with the following Polynomials questions? Thank you very much!

Q1

If x^(3) +2x^(2)y - xy^(2) - 2y^(3) and x^(3) -7xy^(2) - 6y^(3) have (x+2y) as a factor, simplify:

x^(3) +2x^(2)y - xy^(2) - 2y^(3)
__________________________
x^(3) -7xy^(2) - 6y^(3)

Note the factorisation in the denominator can be found be long division by (x + 2y) or by inspection, since you are told (x + 2y) is a factor.

 

[taggs-sasuke]

Yay, thanks!

 

[Drongoski]

Q2