Find zeroes of the polynomial and verify relation between zeroes and coefficients of 2x^2-14
Identifying the zeroes of the polynomial:
- The given polynomial is 2x^2 - 14. To find the zeroes of this polynomial, we need to set the polynomial equal to zero and solve for x.
- 2x^2 - 14 = 0
- 2x^2 = 14
- x^2 = 7
- x = ±√7
Verifying the relation between zeroes and coefficients:
- The relationship between the zeroes of a quadratic polynomial ax^2 + bx + c and its coefficients is given by Vieta's formulas.
- Vieta's formulas state that the sum of the roots of a quadratic polynomial is equal to -b/a and the product of the roots is equal to c/a.
- In the given polynomial 2x^2 - 14, the coefficient of x^2 is 2 (a), the coefficient of x is 0 (b), and the constant term is -14 (c).
- According to Vieta's formulas, the sum of the zeroes is -b/a = 0/2 = 0 and the product of the zeroes is c/a = -14/2 = -7.
- The zeroes we found earlier, ±√7, satisfy the relationship between the zeroes and coefficients of the polynomial.
Therefore, the zeroes of the polynomial 2x^2 - 14 are ±√7 and they satisfy the relationship between the zeroes and coefficients as per Vieta's formulas.