Given that are integers and the two real roots of the equation satisfy

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Given that a,ba,b are integers and the two real roots α,β\alpha,\beta of the equation 3x2+3(a+b)x+4ab=03x^2+3(a+b)x+4ab=0 satisfy α(α+1)+β(β+1)=(α+1)(β+1)\alpha(\alpha+1)+\beta(\beta+1)=(\alpha+1)(\beta+1), find the number of ordered pairs (a,b)(a,b).

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