X square - 2x - 8 find the zeros of the following quadratic polynomial...
Finding Zeros of the Quadratic Polynomial
- To find the zeros of the quadratic polynomial x^2 - 2x - 8, we need to set the polynomial equal to zero and solve for x.
- The equation x^2 - 2x - 8 = 0 can be factored as (x - 4)(x + 2) = 0.
- Setting each factor to zero gives us x - 4 = 0 and x + 2 = 0.
- Solving these equations, we find x = 4 and x = -2.
Verifying Relationship between Zeros and Coefficients
- The relationship between the zeros of a quadratic polynomial and its coefficients is given by Vieta's formulas.
- Vieta's formulas state that for a quadratic polynomial ax^2 + bx + c = 0 with zeros p and q, the sum of the zeros is p + q = -b/a and the product of the zeros is pq = c/a.
- In our case, the sum of the zeros is 4 + (-2) = -b/a = 2, and the product of the zeros is 4 * (-2) = c/a = -8.
- Therefore, the relationship between the zeros 4 and -2 and the coefficients -2 and -8 of the quadratic polynomial x^2 - 2x - 8 is verified by Vieta's formulas.