Nature Of Roots

Question 1

What is the definition of a root in mathematics?

Answer 1

A root of a number is a value that, when raised to a certain power, gives that number.

Question 2

True or False: The square root of a negative number is a real number.

Answer 2

False

Question 3

Fill in the blank: The square root of 16 is _____.

Answer 3

4

Question 4

What is the general form of a quadratic equation?

Answer 4

ax^2 + bx + c = 0

Question 5

Multiple choice: Which of the following numbers is a root of the equation x^2 - 9 = 0? (A) 3 (B) -3 (C) Both A and B (D) None

Answer 5

C

Question 6

What is the relationship between the roots of a polynomial and its coefficients?

Answer 6

The sum and product of the roots of a polynomial are related to its coefficients by Vieta’s formulas.

Question 7

True or False: A polynomial of degree n can have at most n roots.

Answer 7

True

Question 8

What is the term for the highest exponent in a polynomial?

Answer 8

Degree

Question 9

Fill in the blank: The roots of the equation x^3 - 6x^2 + 11x - 6 = 0 are _____.

Answer 9

1, 2, and 3

Question 10

What is a complex root?

Answer 10

A complex root is a root that has both a real part and an imaginary part.