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2x^3 - 5x^2 - 14x + 8
Let P(x) represents the cubic polynomial. We can find the sum of x-values which make P(x) = 0, (the sum of the roots of the equation)
P(x) = 2x^3 - 5x^2 - 14x + 8
P(x) = 0
2x^3 - 5x^2 - 14x + 8 = 0
Since the degree of this polynomial is odd, then the sum of the roots is -[a(n - 1)/an], where a(n-1) is -5 and an is 2. So we have,
-[a(n - 1)/an] = -(-5/2) = 5/2
Thus the sum of the roots is 5/2.
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