Roots Of Polynomials

Question 1

α β γ
How is a basic quadratic set up

Answer 1

X^2 - (sum of the roots)x + (product of the roots)

Question 2

What is the sum of the roots equal to

Answer 2

-b/a

Question 3

What is the product of the roots for a quadratic equal to

Answer 3

C/a

Question 4

(α + β)^2

Answer 4

(α + β)^2 - 2 α β

Question 5

1/α + 1/ β

Answer 5

α + β / α β

Question 6

α^3 + β^3

Answer 6

(α + β)^3 - 3α β(α +β)

Question 7

For a cubic equation what is the equation for the coefficients of x^2

Answer 7

Sum of the roots = -b/a

Question 8

For a cubic equation what is the coefficient of x

Answer 8

Sum of the pairs of roots = c/a

Question 9

For a cubic what is the coefficient of 1

Answer 9

Product of the roots = -d/a

Question 10

For a quartic what is the coefficient of x^3

Answer 10

Sum of the individual roots =-b/a

Question 11

For a quartic what is the coefficient of x^2

Answer 11

Sum of the pairs of roots = c/a

Question 12

For a quartic what is the coefficient of x

Answer 12

Sum of the triples of roots = -d/a

Question 13

For a quartic what is the coeffient of 1

Answer 13

Product of all the roots = e/a