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JEE Main 202523 JanuaryEvening Shift

Exam: JEE Main
Year: 2025
Date: 23 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Sequences and Series

JEE Main 2025 · 23 January · Evening Shift · Mathematics · Sequences and Series

The roots of the quadratic equation 3 x^2-p x+q=0 are 10^ th and...

The roots of the quadratic equation

3 x^2-\mathrm{p} x+\mathrm{q}=0

are

10^{\text{th }}

and

11^{\text{th }}

terms of an arithmetic progression with common difference

\frac{3}{2}

. If the sum of the first 11 terms of this arithmetic progression is 88 , then

q-2 p

is equal to

\qquad

-.

Correct answer

0

Step-by-step solution

\begin{aligned} & S_{11}=\frac{11}{2}(2 a+10 d)=88 \\ & a+5 d=8 \\ & a=8-5 \times \frac{3}{2}=\frac{1}{2} \end{aligned}

Roots are

\begin{aligned} & \mathrm{T}_{10}=\mathrm{a}+9 \mathrm{~d}=\frac{1}{2}+9 \times \frac{3}{2}=14 \\ & \mathrm{~T}_{11}=\mathrm{a}+10 \mathrm{~d}=\frac{1}{2}+10 \times \frac{3}{2}=\frac{31}{2} \\ & \frac{\mathrm{p}}{3}=\mathrm{T}_{10}+\mathrm{T}_{11}=14+\frac{31}{2}=\frac{59}{2} \\ & \mathrm{p}=\frac{177}{2} \\ & \frac{\mathrm{q}}{3}=\mathrm{T}_{10} \times \mathrm{T}_{11}=7 \times 31=217 \\ & \mathrm{q}=651 \\ & \mathrm{q}-2 \mathrm{p} \\ & =651-177 \\ & =474 \end{aligned}

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