Question

Let m and n (m < n) be the roots of the equation x² - 16x + 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?
1. 29
2. 30
3. 32
4. 35

Answer 1

Correct Answer - Option 3 : 32

Calculation:

Given: m and n (m < n) be the roots of the equation x² - 16x + 39 = 0

⇒ x² - 13x - 3x + 39 = 0

⇒ x (x - 13) - 3(x - 13) = (x - 13)× (x - 3) = 0

⇒ x = 13 or 3

⇒ m = 3 and n = 13

∵ m, p, q, r, s and n are in AP

⇒ p + q + r + s = (m + d) + (m + 2d) + (m + 3d) + (m + 4d) = 4m + 10d 2 × (2m + 5d) = 2 × (m + n)

⇒ p + q + r + s = 2 × (2m + 5d) = 2 × (m + n) = 32 ∵ n = m + 5d and m + n = 16