Zeroes, relationship coeff/zeroes, division algorithm MCQs

Q1. An engineer models the height of a fountain jet by x^2 - 8x + 7; at what two horizontal distances does the water return to ground level?

• A.x = 8 and x = 7
• B.x = -1 and x = -7
• C.x = 1 and x = 7
• D.x = 1 and x = -7

Answer: C. x = 1 and x = 7

Factor x^2 - 8x + 7: seek two numbers with product 7 and sum 8. It becomes (x - (1))(x - (7)), giving zeroes x = 1 and x = 7.

Q2. Demand minus supply in a small market is x^2 - 13x + 40; at which two prices does this difference become zero?

• A.x = 5 and x = 8
• B.x = -5 and x = -8
• C.x = 5 and x = -8
• D.x = 13 and x = 40

Answer: A. x = 5 and x = 8

Factor x^2 - 13x + 40: seek two numbers with product 40 and sum 13. It becomes (x - (5))(x - (8)), giving zeroes x = 5 and x = 8.

Q3. A baker finds that daily profit in hundreds of rupees obeys x^2 + 17x + 72; for which two output quantities does this profit vanish?

• A.x = 9 and x = 8
• B.x = -9 and x = -8
• C.x = -9 and x = 8
• D.x = -17 and x = 72

Answer: B. x = -9 and x = -8

Factor x^2 + 17x + 72: seek two numbers with product 72 and sum -17. It becomes (x - (-9))(x - (-8)), giving zeroes x = -9 and x = -8.