Chapter 2: Part A - Roots Of Polynomials.

Question 1

What is the Sum of the roots in a Quadratic equal to?

Answer 1

α + β =** -b/a**.

ax² + bx +c.

Question 2

What is the Product of the roots in a Quadratic equal to?

Answer 2

αβ = c/a.

ax² + bx +c.

Question 3

What is the Sum of the roots in a Cubic equal to?

Answer 3

α + β + γ = -b/a.

ax³ + bx² + cx + d.

Question 4

What is the Sum of the products of the roots in a Cubic equal to?

Answer 4

αβ + βγ + γα = c/a.

ax³ + bx² + cx + d.

Question 5

What is the Product of the roots in a Cubic equal to?

Answer 5

αβγ = -d/a.

ax³ + bx² + cx + d.

Question 6

What is the Sum of the roots in a Quartic equal to?

Answer 6

α + β + γ + δ = -b/a.

ax⁴ + bx³ + cx² + dx + e.

Question 7

What is the Sum of the products of the roots (2 at a time) in a Quartic equal to?

Answer 7

αβ + αγ + αδ + βγ + βδ + γδ = c/a.

ax⁴ + bx³ + cx² + dx + e.

Question 8

What is the Sum of the products of the roots (3 at a time) in a Quartic equal to?

Answer 8

αβγ + βγδ + γδα + δαβ = -d/a.

ax⁴ + bx³ + cx² + dx + e.

Question 9

What is the Product of the roots in a Quartic equal to?

Answer 9

αβγδ = e/a.

ax⁴ + bx³ + cx² + dx + e.

Question 10

What is the formula to find α² + β²?

Answer 10

α² + β² = (α + β)² - 2αβ.