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Let p and q be the two distinct real roots of x² + 20x - 2020 = 0, and let r and s be the two distinct complex roots of x² - 20x + 2020 = 0. Evaluate: p*r*(p - r) + p*s*(p - s) + q*r*(q - r) + q*s*(q - s).

1. 0
2. 8000
3. 8080
4. 16000

Correct answer: 16000

Solution

Expanding gives (p² + q²)(r+s) - (p+q)(r²+s²). With p+q = -20, pq = -2020, r+s = 20, rs = 2020: p²+q² = 400+4040 = 4440; r²+s² = 400-4040 = -3640. Result = 4440*20 - (-20)*(-3640) = 88800 - 72800 = 16000.

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