The roots of the equation x 2 +px+q=0 are 1 and 2, the roots of the equation qx 2 -px+1=0 must be

The correct answer is C, the roots being -1 and -1/2. The options were not included with the question, so the match rests on the roots themselves.

For x² + px + q = 0 with roots 1 and 2, Vieta's formulas give sum of roots = -p, so 3 = -p, giving p = -3. Product of roots = q, so q = 2.

Substituting into qx² - px + 1 = 0 gives 2x² + 3x + 1 = 0. Factorising gives (2x + 1)(x + 1) = 0, so x = -1/2 or x = -1.

• Options with 1 or +1/2 as a root ignore the sign of p. Using p = +3 instead of -3 flips the signs of the roots.
• Options with a single root correct usually come from a sign slip in only one factor.

This is a standard Vieta's formulas application, and it links to quadratic equations in the Prelims Mathematics and Reasoning section and to quick algebraic manipulation in Mains answers.

Trap: writing p = 3 directly from the coefficient. Sum of roots is -p, so always check the sign before substituting.