Solving quadratics writing solutions

Question

I am confused on the notation used when writing down the solution of x and y in quadratic equations. For example in $x^2+2x-15=0$, do I write :

$x=-5$ AND $x=3$

or is it

$x=-5$ OR $x=3$

which is it and why? I thought that because x can only equal one of the values when you substitute it in so it would be OR, however there are sometimes 2 roots of a quadratic so is it more correct to use AND? What about for the value of $y$, is it the same?

Thanks in advance

Answer 1

It depends on the context. Consider these two examples:

• The solutions to $x^2+2x-15=0$ are $x=-5$ and $x=3$.

• If $x^2+2x-15=0$ then $x=-5$ or $x=3$.

In both cases, it would be wrong to use 'or' in stead of 'and' or 'and' in stead of 'or'.

Answer 2

Firstly, it's impossible that $x=-5$ and $x=3$.

We need to solve $$(x+5)(x-3)=0,$$ which gives $$x+5=0$$ or $$x-3=0$$ and from here we get a right answer.

Actually, to solve an equation with one variable it says to find a full set of the roots.

You can say that $-5$ and $3$ they are roots of the equation and we see that our equation has no another roots.