Roots of Polynomials

Question 1

In the form,
When a =1, what is the sum of the roots? What is the product of the roots?

Answer 1

Question 2

If alpha and beta are the roots of a quadratic, write the equation I’m terms of alpha beta

Answer 2

Question 3

Answer 3

If ā is the root of a quadratic equation with real coefficients and ā is a complex number, then the other root must be it’s complex conjugate (ā)*.

Question 4

Answer 4

Question 5

Sum of roots and products of roots when a!=1

Answer 5

Question 6

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Question 7

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Question 8

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Question 9

Answer 9

Question 10

What are the scenarios of the roots of a cubic graph (complex and real)?

Answer 10

Complex roots always occur in a pair

Question 11

What is the roots of cubics shortcuts?

Answer 11

Question 12

Answer 12

Question 13

Solve using shortcuts

Answer 13

Question 14

Solve using subtraction method

Answer 14

Question 15

What is the relationship between quartics Co efficient and roots

Answer 15

Question 16

what is the sum of the square of the roots?

Answer 16

Question 17

Answer 17

Question 18

what are some mark scheme must dos?

Answer 18

• include ‘=0’
• must show full method used when getting factors from an equation

Question 19

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Question 20

Answer 20

Question 21

Answer 21

Question 22

How do you show roots on an Argand diagram?

Answer 22

1. Label axis as Re(z) and Im(z)
2. Plot roots and write the root out instead of a coordinate (3+i)
3. Draw a line from the origin to the point

Question 23

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Question 24

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Question 25

Answer 25