Vieta's Theorem Review

What is Vieta's theorem?

• Vieta's theorem relates the coefficients of a polynomial to sums and products of its roots.

• Vieta's theorem is a historical theorem about the Roman Empire

• Vieta's theorem is a law of physics related to energy conservation

• Vieta's theorem is a geometric theorem about the angles of a triangle

State Vieta's formulas for a quadratic equation.

• The sum of the roots is -b/a and the product of the roots is c/a

• The sum of the roots is -a/b and the product of the roots is c/a

• The sum of the roots is b/a and the product of the roots is -c/a

• The sum of the roots is a/b and the product of the roots is -c/a

If the sum of the roots of a quadratic equation is 5 and the product of the roots is 6, what is the equation?

• (x - 5)(x - 1) = 0

• (x + 2)(x + 3) = 0

• (x - 2)(x - 3) = 0

• (x - 1)(x - 6) = 0

If the sum of the roots of a cubic equation is 10 and the product of the roots is -15, what is the equation?

• x^3 - 10x^2 - 15x - 50 = 0

• x^3 + 10x^2 - 15x - 50 = 0

• x^3 - 10x^2 + 15x - 50 = 0

• x^3 - 10x^2 - 15x + 50 = 0

Find the sum of the roots of the equation x^2 - 6x + 9 = 0.

• -3

• 6

• 9

• 3

Find the product of the roots of the equation 2x^2 + 5x - 3 = 0.

• -3/2

• -1/3

• 3/2

• 1/2

If the sum of the roots of a quartic equation is 7 and the product of the roots is -10, what is the equation?

• The quartic equation is x^4 - 7x^3 - 10x^2 + 70x - 100 = 0

• The quartic equation is x^4 - 10x^3 - 7x^2 + 70x - 100 = 0

• The quartic equation is x^4 - 7x^3 - 10x^2 + 70x + 100 = 0

• The quartic equation is x^4 - 7x^3 - 10x^2 - 70x + 100 = 0

If the sum of the roots of a quintic equation is -4 and the product of the roots is 12, what is the equation?

• The quintic equation is x^5 + 4x^4 + 12x^3 - 48x^2 - 144x - 576 = 0

• The quintic equation is x^5 - 4x^4 + 12x^3 - 48x^2 + 144x - 576 = 0

• The quintic equation is x^5 + 4x^4 - 12x^3 - 48x^2 + 144x + 576 = 0

• The quintic equation is x^5 - 4x^4 - 12x^3 + 48x^2 - 144x - 576 = 0

Find the sum of the roots of the equation 3x^2 - 4x - 8 = 0.

• 2/3

• 3/4

• -(-4)/3 = 4/3

• 5/6

Find the product of the roots of the equation 4x^2 + 9x + 2 = 0.

• 1/4

• 2

• -2

• -1/4