#Past paper question.

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quartz kettleBOT
tulip tide
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The highest degree of the equation is maximum no. of real distinct roots it can have

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It may have less than 3, but you'll have to solve it to find that, which you can't here

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I don't know if there's a way to find out the nature of the roots without solving anything

warm vapor
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There is a cubic discriminant but I'm not sure that's the most elegant way of doing it

empty thicket