The roots of the quadratic equation $3x^2-px+q=0$ are $10^{th}$ and $11^{th}$ terms of an arithmetic progression with common difference $\frac32$. If the sum of the first 11 terms of this arithmetic progression is 88, then $q-2p$ is equal to ______ -.

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $S_{11}=\frac{11}2(2a+10d)=88\Rightarrow2a+15=16$, $a=\frac12$. $a_{10}=\frac12+9\cdot\frac32=14$ and $a_{11}=15.5$. $\frac p3=14+15.5=29.5\Rightarrow p=88.5$ and $\frac q3=14	imes15.5=217\Rightarrow q=651$. $q-2p=651-177=474$. Answer: 474.

Q. The roots of the quadratic equation $3x^2-px+q=0$ are $10^{th}$ and $11^{th}$ terms of an arithmetic progression with common difference $\frac32$. If the sum of the first 11 terms of this arithmetic progression is 88, then $q-2p$ is equal to ______ -.

Explanation

Reviewed by Dr. Abubacker

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