1. ## I just need an explanation for this please?

I am factorising polynomials of higher degrees, and doing some questions for practice. There is a section where the instruction was: 'Solve each equation in the real number system..' what does that mean? is it just to solve it using the various steps that we learnt? or does it mean something more, or something specific.

Also what is the 'multiplicity'??

I didn't get an explanation for this..

Can anyone help?

2. Originally Posted by Ife
I am factorising polynomials of higher degrees, and doing some questions for practice. There is a section where the instruction was: 'Solve each equation in the real number system..' what does that mean? is it just to solve it using the various steps that we learnt? or does it mean something more, or something specific.

Also what is the 'multiplicity'??

I didn't get an explanation for this..

Can anyone help?
It means solve in the usual way - your answers may contain surds.

But you're not allowed to have answers that are not real numbers eg. square root of negative numbers.

3. thanks.. i thought it was something like that.. what about the 'multiplicity' part?

4. Originally Posted by Ife
thanks.. i thought it was something like that.. what about the 'multiplicity' part?
I suppose they mean the number of times a solution appears. eg. The solutions to (x-1)^2(x+2) = 0 are x = 1, 1 and -2. So the solution x = 1 has a multiplicity of two.

5. "'Solve each equation in the real number system.." means specifically "find all real number solutions". For example, the equation $\displaystyle x^3- x^2+ x- 1= 0$, which can be factored as $\displaystyle (x-1)(x^2+ 1)= 0$ has real root 1. There are no real numbers that make $\displaystyle x^2+ 1= 0$.