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## 1. Viète Theorem In the quadratic equation

• 1, If x1 and x2 are two roots of the quadratic equation: ax2+bx+c=0(a≠0) , we have:
• S = x 1 + x 2 = -b / a
• P = x 1*x 2 = c / a
• 2, If a + b + c = 0 => the quadratic equation has a root equal to 1.
• 3, If a – b + c =0 => the quadratic equation has a root equal to -1.
• 4, The quadratic equation has two distinct roots with the same sign <=> Δ > 0 and P > 0.
• 5, The equation has two distinct roots with the opposite in sign <=>Δ > 0 and P < 0.
• 6, The equation has two distinct roots of the same positive <=> Δ > 0, S > 0 and P > 0.
• 7, The equation has two distinct roots of the same negative <=> Δ > 0, S < 0 and P > 0.

## 2. Viète Theorem in the cubic equation

• If x1, x2, and x3 are three roots of the cubic equation: ax3+bx2+cx+d=0 (a≠0) , we have:
• Firstly, x 1 + x 2 + x 3= -b / a
• Next, x 1 * x 2 + x 2 * x 3 + x 3 * x 1 = c / a
• Finally, x 1 * x 2 * x 3 = -d / a