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The roots of the quadratic equation 3 x^2- p x+ q =0 are 10^ th and 11^ th terms of an arithmetic progression with common difference 3 2 . If the sum of the first 11 terms of this arithmetic progression is 88 , then q-2 p is equal to -.

Correct answer

0

Step-by-step solution

aligned & S₁₁= 11 2 (2 a+10 d)=88 & a+5 d=8 & a=8-5 3 2 = 1 2 aligned Roots are aligned & T ₁₀= a +9 ~d = 1 2 +9 3 2 =14 & ~T ₁₁= a +10 ~d = 1 2 +10 3 2 = 31 2 & p 3 = T ₁₀+ T ₁₁=14+ 31 2 = 59 2 & p = 177 2 & q 3 = T ₁₀ T ₁₁=7 31=217 & q =651 & q -2 p & =651-177 & =474 aligned

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