Zeros of Polynomials Quiz

Question 1

What is meant by zeros of simultaneous polynomials?

Accepted Answer

Values that make both polynomials zero

Answer

Coefficients of polynomials

Answer

Degree of polynomials

Answer

Values that make one polynomial zero

Question 2

If p(x) and q(x) have simultaneous zeros, what will be their common factor?

Accepted Answer

(x - a) where a is the simultaneous zero

Answer

Only constant term

Answer

x²

Answer

(x + a) where a is a coefficient

Question 3

Which method is used to find simultaneous zeros of two polynomials?

Accepted Answer

Euclidean Division Algorithm

Answer

Synthetic Division

Answer

Lagrange Interpolation

Answer

Quadratic Formula

Question 4

If p(x) = x² - 5x + 6 and q(x) = x - 2, what is their simultaneous zero?

Accepted Answer

x = 2

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 5

What do the zeros of GCD of two polynomials represent?

Accepted Answer

Simultaneous zeros

Answer

Only zeros of second polynomial

Answer

Only zeros of first polynomial

Answer

All possible zeros

Question 6

If GCD of two polynomials is 1, how many simultaneous zeros will they have?

Accepted Answer

None (0)

Answer

Two

Answer

Infinite

Answer

One

Question 7

What are the zeros of polynomial p(x) = x³ - 6x² + 11x - 6?

Accepted Answer

1, 2, 3

Answer

1, 3, 5

Answer

1, 2, 4

Answer

2, 3, 4

Question 8

If p(x) = (x-1)(x-2) and q(x) = (x-2)(x-3), what is their simultaneous zero?

Accepted Answer

x = 2

Answer

x = 1

Answer

x = 1, 2, 3

Answer

x = 3

Question 9

Which algebraic technique is used to find simultaneous zeros?

Accepted Answer

Greatest Common Divisor (GCD) method

Answer

Least Common Multiple (LCM) method

Answer

Factor Theorem

Answer

Remainder Theorem

Question 10

If p(x) = x² - 4 and q(x) = x² - 2x, what is their simultaneous zero?

Accepted Answer

x = 2

Answer

x = 4

Answer

x = 0

Answer

x = -2

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