Polynomials — Practice Quiz
Karnataka Board · Class 10 · Mathematics
Try a 4-question quiz on Polynomials for Karnataka Board Class 10 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Polynomials
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What is the degree of the polynomial 3x² - 7x + 2?
Which of the following is a linear polynomial?
Find the zero of the linear polynomial 4x - 12.
If p(x) = x² - 5x + 6, what is p(2)?
Sample Questions
Which expression is NOT a polynomial?
Show answer
1/x + 3
Step 1: A polynomial must have non-negative integer powers of x. Step 2: Check each option: 3x² + 2x - 1 has powers 2, 1, 0 (all valid). Step 3: 1/x + 3 = x⁻¹ + 3 has power -1 (negative power). Step 4: 5x³ - x + 7 and 2x - 9 have valid powers. Therefore, 1/x + 3 is NOT a polynomial.
The zeroes of x² - 7x + 12 are:
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3 and 4
Step 1: Factor x² - 7x + 12. We need two numbers that multiply to 12 and add to -7. Step 2: The numbers are -3 and -4 since (-3) × (-4) = 12 and (-3) + (-4) = -7. Step 3: x² - 7x + 12 = (x - 3)(x - 4). Step 4: Set each factor to zero: x - 3 = 0 gives x = 3, and x - 4 = 0 gives x = 4. Therefore, the zeroes are 3 and 4.
For the polynomial 2x² + 3x - 5, what is the sum of the zeroes?
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-3/2
Step 1: For a quadratic polynomial ax² + bx + c, the sum of zeroes = -b/a. Step 2: Compare 2x² + 3x - 5 with ax² + bx + c: a = 2, b = 3, c = -5. Step 3: Sum of zeroes = -b/a = -3/2. Step 4: Therefore, the sum of the zeroes is -3/2.
For the polynomial x² - 4x + 3, what is the product of the zeroes?
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3
Step 1: For a quadratic polynomial ax² + bx + c, the product of zeroes = c/a. Step 2: Compare x² - 4x + 3 with ax² + bx + c: a = 1, b = -4, c = 3. Step 3: Product of zeroes = c/a = 3/1 = 3. Step 4: Therefore, the product of the zeroes is 3.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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