#Past paper question.
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The highest degree of the equation is maximum no. of real distinct roots it can have
It may have less than 3, but you'll have to solve it to find that, which you can't here
I don't know if there's a way to find out the nature of the roots without solving anything
There is a cubic discriminant but I'm not sure that's the most elegant way of doing it
if you know calculus, you can use derivatives (as shown here) https://www.youtube.com/watch?v=-500F5Afmyk