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Rahul says he has a quadratic polynomial whose two zeroes are BOTH POSITIVE, with sum of zeroes −7 and product of zeroes 12.
Where does his reasoning break down?

Class 10Zeroes and CoefficientsAlgebra — Polynomials
  • AThe product should be negative when both zeroes are positive
  • BNo quadratic polynomial can have sum of zeroes −7 and product of zeroes 12
  • CThe sum of two positive numbers cannot be negative — the zeroes are actually −3 and −4
  • DNothing breaks down; the zeroes are 3 and 4

Step-by-Step Solution

Two positive numbers always add to a positive number, so a sum of −7 rules out a positive pair. The polynomial itself is fine: has zeroes −3 and −4, which add to −7 and multiply to 12 — both facts consistent, both zeroes negative. Only Rahul’s claim that they are positive fails. The first option is backwards (two negatives multiply to a positive); the last option gives the zeroes of , whose sum is +7.
Answer: C) The sum of two positive numbers cannot be negative — the zeroes are actually −3 and −4

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