Match the following columns: Quadratic Equation Relation Between Roots 1. p² – 6p - 27 = 0 A. Both roots are negative. 2. q² + 16q + 63 = 0 B. The difference between both roots is 12. 3. r² + 8r – 20 = 0 C. The sum of squares of roots is 90.

By Vieta's formulas, the sum and product of roots for p squared minus six p minus twenty seven are six and negative twenty seven, meaning the roots are nine and negative three, whose squares sum to ninety to match relation C. For q squared plus sixteen q plus sixty three, the positive sum and product indicate both roots are negative, matching relation A. The equation r squared plus eight r minus twenty equals zero has roots of negative ten and two, giving a difference of twelve to match relation B; therefore, the correct match is one to C, two to A, and three to B.

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