polynomials cubic function (1 Viewer)

[jp92]

hey people i was just wondering if the general shape of a cubic function P(x)=0 with roots a, b and c have the form of:

P(x)=x^3-(a+b+c)x^2+(ab+ac+bc)x-abc

???

 

[addikaye03]

hey people i was just wondering if the general shape of a cubic function P(x)=0 with roots a, b and c have the form of:

P(x)=x^3-(a+b+c)x^2+(ab+ac+bc)x-abc

???

Well:

Cubic Polynomial would have at most 3 roots .'.

P(x)=(x-a)(x-b)(x-c) where a,b,c are roots of P(x)

RHS= (x^2-ax-bx+ab)(x-c)

=x(x^2-ax-bx+ab)-c(x^2-ax-bx+ab)

=x^3-ax^2-bx^2+abx-cx^2+acx+bcx-abc

=x^3-(a+b+c)x^2+(ab+ac+bc)x-abc #

So you are correct! But there's the derivation for you

 

[jp92]

thanks for your help