Quadratic Equation Roots in GP | JEE Maths Question

Maths 08: Quadratic Equations and Roots in Geometric Progression

Quadratic Equations are an important part of JEE Mathematics. Questions that combine the roots of two quadratic equations with sequences such as Geometric Progression test both conceptual understanding and algebraic accuracy.

In this Maths 08 question, α and β are the roots of one quadratic equation, while γ and δ are the roots of another. The four roots α, β, γ and δ form a Geometric Progression with a positive common ratio. Students must use the relationship between roots and coefficients to calculate the required value.

Important Concepts Used

For the quadratic equation:

ax² + bx + c = 0

If its roots are α and β, then:

α + β = −b/a

αβ = c/a

These relationships are known as Vieta’s formulas.

Roots in Geometric Progression

If α, β, γ and δ are consecutive terms of a Geometric Progression, they may be represented as:

a, ar, ar², ar³

where:

• a is the first term
• r is the common ratio
• r is positive in the given question

The sums and products of these roots can then be connected to the coefficients of the two quadratic equations.

How to Approach the Question

1. Find α + β from the first equation
2. Find γ + δ from the second equation
3. Represent the four roots as consecutive GP terms
4. Compare the two sums to determine the common ratio
5. Use root products to calculate p and q
6. Simplify p + q
7. Match the result with the correct option

Important JEE Points

• Read the signs of coefficients carefully
• Apply the sum and product of roots correctly
• Preserve the exact order of the GP terms
• Use the condition that the common ratio is positive
• Avoid solving each quadratic equation separately unless necessary
• Simplify fractional values only after completing the substitution

Watch the complete Maths 08 video for the step-by-step calculation and correct option.

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