Q1:jipmat 2025QA › Quadratic EquationsMediumQA · MCQ

Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots (4, 3). Alok made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of the equation are:

• A-4, -3
• B6, 1
• C4, 3
• D-6, -1

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The Setup: We are reconstructing a standard quadratic equation $x^2+bx+c=0$. If you fumble the constant ($c$), your sum of roots ($-b$) is still safe. If you fumble the $x$ coefficient ($b$), your product of roots ($c$) remains a W. Step 1: Analyze Amit's work. He messed up the constant term, meaning his sum of roots is straight facts. Roots: $4$ and $3$. Sum of roots $=4+3=7$. Since sum of roots $=-b$, we get $b=-7$. Step 2: Analyze Alok's work. He messed up the $x$ coefficient, meaning his product of roots is legit. Roots: $3$ and $2$. Product of roots $=3 \times 2=6$. Since product of roots $=c$, we get $c=6$. Step 3: Build the correct equation and solve it like a boss. Equation: $x^2-7x+6=0$. Factorizing: $(x-6)(x-1)=0$. Correct roots are $6$ and $1$. Final Answer: 6, 1