Polynomials (Class 10 Mathematics)

Polynomials are algebraic expressions with multiple terms consisting of variables and constants. Understanding polynomial operations and theorems like the

Polynomials (Class 10 Mathematics)

Polynomials are algebraic expressions with multiple terms consisting of variables and constants. Understanding polynomial operations and theorems like the

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TL;DR: Polynomials are algebraic expressions with multiple terms consisting of variables and constants. Understanding polynomial operations and theorems like…

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Polynomials are algebraic expressions with multiple terms consisting of variables and constants. Understanding polynomial operations and theorems like the

Polynomials MCQs with Answers & Explanations

Q1. If x = 2 is a zero of the polynomial p(x) = x^2 - 2x + k, then k is:

  1. 0 ✓ (correct)
  2. 2
  3. 4
  4. -2

Explanation: If x = 2 is a zero, then p(2) = 0. So 4 - 4 + k = 0, which gives k = 0.

Q2. The degree of the polynomial 4x^3 - 5x^2 + 2x - 1 is:

  1. 1
  2. 3 ✓ (correct)
  3. 4
  4. 2

Explanation: The degree of a polynomial is the highest power of the variable, which is 3 in this case.

Q3. If the sum of zeros of the polynomial x^2 - 5x + 6 is s, then s is:

  1. 3
  2. 6
  3. 5 ✓ (correct)
  4. -5

Explanation: For a quadratic ax^2 + bx + c, sum of zeros = -b/a = -(-5)/1 = 5.

Q4. The product of zeros of the polynomial 2x^2 - 8x + 6 is:

  1. -4
  2. -3
  3. 4
  4. 3 ✓ (correct)

Explanation: For a quadratic ax^2 + bx + c, product of zeros = c/a = 6/2 = 3.

Q5. When p(x) = x^3 - 2x^2 + x - 1 is divided by (x - 1), the remainder is:

  1. -1 ✓ (correct)
  2. 0
  3. -2
  4. -3

Explanation: By the Remainder Theorem the remainder is p(1) = 1 - 2 + 1 - 1 = -1.

Q6. Which of the following is a factor of x^3 - 8?

  1. x + 2
  2. x - 2
  3. x^2 + 2x + 4
  4. All of the above ✓ (correct)

Explanation: x^3 - 8 = (x - 2)(x^2 + 2x + 4), so all three are factors of this polynomial.

Q7. The number of zeros of a cubic polynomial is at most:

  1. 1
  2. 3 ✓ (correct)
  3. 4
  4. 2

Explanation: A polynomial of degree n has at most n zeros. A cubic polynomial has degree 3, so it has at most 3 zeros.

Q8. If (x - 1) is a factor of x^3 + ax^2 - 2x - 1, then a is:

  1. 0
  2. 1
  3. 2 ✓ (correct)
  4. -1

Explanation: If (x - 1) is a factor, then p(1) = 0. So 1 + a - 2 - 1 = 0, which gives a = 2.

Q9. The zeros of the polynomial (x - 3)(x + 2)(x - 1) are:

  1. -3, -2, -1
  2. 3, 2, 1
  3. -3, 2, -1
  4. 3, -2, 1 ✓ (correct)

Explanation: The zeros are the values of x that make the polynomial equal to 0, which are 3, -2, and 1.

Q10. If the polynomial x^2 - px + q has zeros a and b, then:

  1. a + b = p, ab = q ✓ (correct)
  2. a + b = -p, ab = -q
  3. a + b = p, ab = -q
  4. a + b = q, ab = p

Explanation: By Vieta's formulas, sum of zeros = p and product of zeros = q for the polynomial x^2 - px + q.

Frequently Asked Questions

What is the remainder theorem and how is it used?

The remainder theorem states that when a polynomial p(x) is divided by (x - a), the remainder is p(a).

How do you determine if a number is a zero of a polynomial?

A number is a zero of a polynomial if substituting it for the variable makes the polynomial equal to zero.

More Class 10 Mathematics MCQs

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