Vieta's Formulas are mathematical equations that relate the coefficients of a polynomial to sums and products of its roots. For a quadratic polynomial of the form ax^2 + bx + c = 0 , the formulas state that the sum of the roots (denoted as r_1 + r_2 ) is equal to -b/a, and the product of the roots (denoted as r_1 \cdot r_2 ) is equal to c/a . These relationships extend to higher-degree polynomials as well. For a cubic polynomial ax^3 + bx^2 + cx + d = 0 , the sum of the roots is -b/a, the sum of the products of the roots taken two at a time is c/a , and the product of the roots is -d/a. Vieta's Formulas provide a powerful tool for analyzing polynomial equations without needing to find