Polynomials (10 Mathematics)
Polynomials are algebraic expressions with terms containing variables raised to non-negative integer powers. Understanding zeros, factors, and the relation
TL;DR: Polynomials are algebraic expressions with terms containing variables raised to non-negative integer powers. Understanding zeros, factors, and the rel…
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Polynomials are algebraic expressions with terms containing variables raised to non-negative integer powers. Understanding zeros, factors, and the relation
Polynomials MCQs with Answers & Explanations
Q1. A polynomial of degree 2 is called:
- Linear
- Quadratic ✓ (correct)
- Cubic
- Quartic
Q2. If (x - 2) is a factor of polynomial p(x), then p(2) equals:
- 2
- 1
- 0 ✓ (correct)
- -1
Q3. The zeros of the polynomial x² - 5x + 6 are:
- 1 and 6
- 2 and 3 ✓ (correct)
- -2 and -3
- 5 and 6
Q4. If α and β are zeros of ax² + bx + c, then α + β equals:
- c/a
- -b/a ✓ (correct)
- b/a
- -c/a
Q5. The remainder when p(x) = x³ + 2x² - x + 1 is divided by (x - 1) is:
- 0
- 1
- 2
- 3 ✓ (correct)
Q6. A cubic polynomial has at most ____ zeros.
- 1
- 2
- 3 ✓ (correct)
- 4
Q7. If the zeros of a polynomial are 1, 2, and 3, the polynomial is:
- (x-1)(x-2)(x-3) ✓ (correct)
- (x+1)(x+2)(x+3)
- (x-1)² + (x-2)² + (x-3)²
- x³ - x² - x + 3
Q8. The product of zeros of ax² + bx + c equals:
- -b/a
- c/a ✓ (correct)
- b/c
- -c/a
Q9. Which polynomial has a zero at x = -1?
- x² + 1
- x² - 1 ✓ (correct)
- x² + x + 1
- x² - x + 1
Q10. The degree of the polynomial (x+1)³(x-2)²(x+3) is:
- 3
- 4
- 5
- 6 ✓ (correct)
Frequently Asked Questions
What is the Factor Theorem and how is it useful?
The Factor Theorem states that (x - a) is a factor of p(x) if and only if p(a) = 0. It's useful for finding zeros and factoring polynomials without lengthy division.
How can Vieta's formulas help solve problems?
Vieta's formulas relate the coefficients of a polynomial to the sum and product of its zeros. For a quadratic ax² + bx + c with zeros α and β: α + β = -b/a and αβ = c/a. This helps find zeros or construct polynomials from given zeros.
More 10 Mathematics MCQs
- Coordinate Geometry
- Arithmetic Progressions
- Circles
- Surface Areas and Volumes
- Trigonometry (Applications Case Study)
- Probability (Case Study)
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