AMC / AIME · Quadratics · Hard

Quadratics: For how many integers math does math have integer roots?

Factor and complete square.

Try the problem

For how many integers nn does x2−nx+12=0x^2-nx+12=0 have integer roots?

Hint and answer

Concept to use

Parameter ranges.

Hint

Use factoring, Vieta's relations, or the discriminant.

Answer

6

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