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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Sequences and Series

NDA 2019 · Mathematics · Sequences and Series

Let m and n(m < n) be the roots of the equation x^2-16 x+39=0 . If...

Let mm and n(m<n)n(m < n) be the roots of the equation x2−16x+39=0x^2-16 x+39=0. If four terms p,q,rp, q, r and ss are inserted between m and nn to form an AP , then what is the value of p+q+r+sp+q+r+s ?

Options

  1. A29
  2. B30
  3. C32
  4. D35

Correct answer

C. 32

Step-by-step solution

x2−16x+39=0⇒x2−13x−3x+39=0⇒(x−13)(x−3)=0⇒ Roots are 3 and 13.\begin{aligned} & 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 Pbetween3and13hascommondifference=between 3 and 13 has common difference =\frac{b-a}{n+1}⇒d=\Rightarrow d=\frac{13-3}{5}=2∴AP2\therefore A P between 3 and 13 is 5,7,9,11∴ sum =5+7+9+11=32\begin{aligned} & 5,7,9,11 \\ ∴ \text{ sum }=5+7+9+11 \\ & =32 \end{aligned}
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