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Let m and n(m 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 ?

Options

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

Correct answer

C. 32

Step-by-step solution

aligned & x^2-16 x+39=0 & x^2-13 x-3 x+39=0 & (x-13)(x-3)=0 & Roots are 3 and 13 . aligned A P between 3 and 13 has common difference = b-a n+1 d= 13-3 5 =2 A P between 3 and 13 is aligned & 5,7,9,11 ∴ sum =5+7+9+11 & =32 aligned

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