In a cubic polynomial 2xxx-5xx-14x 8 find the sum of the zeros?

Answer 1

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.