Consider the quadratic equation (n²-2n+2)x²-3x+(n²-2n+2)²=0, n R. Let α be the minimum value of the product of its roots and β be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is α and the common ratio is (α)/(β), is:

Sequence and Series: JEE Main 2026 Mathematics question

JEE Main 2026 · 6 Apr, Evening shift · Q2

JEE Main 20266 Apr, Evening shiftMathematicsMediumSequence and Series179× since 2002

Consider the quadratic equation

(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0

n \in \mathbf{R}

. Let

\alpha

be the minimum value of the product of its roots and

\beta

be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is

\alpha

and the common ratio is

\dfrac{\alpha}{\beta}

, is :