Q165 / 270 · NDA 2019 (Phase 2) · Mathematics

Let $m$ and $n(m \lt n)$ be the roots of the equation $x^2-16 x+39=0$. If four terms $p, q, r$ and $s$ are inserted between m and $n$ to form an AP , then what is the value of $p+q+r+s$ ?

  • A
    29
  • B
    30
  • Correct answer
    C
    32
  • D
    35

Solution

$\begin{aligned} & \text {} x^2-16 x+39=0 \\ & \Rightarrow x^2-13 x-3 x+39=0 \\ & \Rightarrow(x-13)(x-3)=0 \\ & \Rightarrow \text { Roots are } 3 \text { and } 13 . \end{aligned}$ $A P$ between 3 and 13 has common difference $=\frac{b-a}{n+1}$ $\Rightarrow d=\frac{13-3}{5}=2$ $\therefore A P$ between 3 and 13 is $\begin{aligned} & 5,7,9,11 \\ ∴ \text { sum }=5+7+9+11 \\ & =32 \end{aligned}$

Hence, the correct answer is option: 'C'.

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