Silly Question on Definition of real solutions and real roots

Question

For $a\neq0$, the equation $ax^2+b|x|+c=0$ has k real solutions and p real roots.

Here, my doubt is what does the solution means and how it is different from real roots?

Thanks for clearing my silly doubt.

Answer 1

They're the same.

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If you want to be super pedantic – don't be – the equation has solutions, not roots.

For those who like getting into pointless arguments, there's a reasonable case that a function has roots and no solutions, whereas an equation has solutions but no roots. But that's fighting the same sort of losing battle as the one fights who argues that "data" is a plural and not a mass noun; everyone is sure to ignore you if you try and impose this as a rule of grammar. You'd have a better chance of convincing people that "awesome" means "terrible and mighty" and not "brilliant and wonderful".