Multiple choice

Suppose a, b denote the distinct real roots of the quadratic polynomial x2 + 20x - 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x2 - 20x + 2020. Then the value of ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) is

  1. 0

  2. 8000

  3. 8080

  4. 16,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The expression is (ac + ad + bc + bd)(a-c)(a-d)(b-c)(b-d) is not the right approach. The expression is symmetric. Using Vieta's formulas for the roots, the value evaluates to 16,000.

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