CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

The question is about Sum and product of the roots of a Quadratic Equation. Some details about the product and sum of the roots are given and we need to find out the product of the roots. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 11: Sum of the roots of a quadratic equation is 5 less than the product of the roots. If one root is 1 more than the other root, find the product of the roots?

1. 6 or 3
2. 12 or 2
3. 8 or 4
4. 12 or 4

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Quadratic Equations: Knowledge about the product and sum of the roots is important to solve this one!!

Sum of the roots = (product of the roots) – 5
Let r₁ and r₂ be the two roots
r₁ = r₂ + 1

Therefore,
r₁ + 1 + r₂ = (r₁r₂) * r₂ - 5
r₂ + 1 + r₂ = (r₂ + 1) * r₂ - 5
2r₂ + 6 = (r₂)² + r₂
(r₂)² - r₂ - 6 = 0
Solving, we get r₂ = 3 or -2
Therefore, r₂ = 4 or -1

Hence product of the two roots is either 12 or 2.

The question is "If one root is 1 more than the other root, find the product of the roots?"

Hence the answer is "12 or 2"

Choice B is the correct answer.