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If (alpha) and (beta) are the roots of the equation (2x^{2} + 5x + n…

If (alpha) and (beta) are the roots of the equation (2x^{2} + 5x + n = 0), such that (alphabeta = 2), find the value of n.

  • A.
    -4
  • B.
    -2
  • C.
    2
  • D.
    4
Correct Answer: Option D
Explanation

An equation can be written as (x^{2} – (alpha + beta)x + (alphabeta) = 0)

Making the coefficient of (x^{2}) = 1 in the given equation, we have

(x^{2} + frac{5}{2}x + frac{n}{2} = 0)

Comparing, we have (alphabeta = frac{n}{2} = 2 implies n = 4)