Roots of polynomials
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13 Terms
What is the equation for the sum of the roots of a quadratic?
-b/a
What is the equation for the product of the roots of a quadratic?
c/a
What is the equation for the sum of the roots of a cubic?
-b/a
What is the equation for the sum of the product pairs of a cubic?
c/a
What is the equation for the product of the roots of a cubic?
-d/a
What is the equation for the sum of all the roots of a quartic?
-b/a
What is the equation of the sum of all the product pairs of a quartic?
c/a
What is the equation for the sum of all the product triplets of a quartic?
-d/a
What is the equation for the product of the roots of a quartic?
e/a
What is the formula for the sum of the reciprocals of the roots for all three?
Quadratic - Sum of roots / product of roots
Cubic - Sum of product pairs / product of roots
Quartic - Sum of product triplets / product of roots
For a quadratic, what is the sum of (alpha)2 + (beta)2?
(Sum of roots)2 - 2(product of roots)
For a cubic, what is the sum of (alpha)2 + (beta)2 + (gamma)2?
(Sum of roots)2 - 2(Sum of product pairs)
For a quartic, what is the sum of (alpha)2 + (beta)2 + (gamma)2 + (sigma)2?
(Sum of roots)2 - 2(Sum of product pairs)