Polynomials And Equations — Important Questions
Kerala Board · Class 10 · Mathematics
44 important questions from Polynomials And Equations for Kerala Board Class 10 Mathematics, with answers. Written for the board exams 2027.
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Important Questions from Polynomials And Equations
Which of the following are correct factorizations? (Select all that apply)
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x² + 7x + 12 = (x + 3)(x + 4), x² - 5x + 6 = (x - 2)(x - 3), x² + x - 6 = (x + 3)(x - 2), x² + 5x - 6 = (x + 6)(x - 1)
Check each by expanding: (x + 3)(x + 4) = x² + 7x + 12 ✓, (x - 2)(x - 3) = x² - 5x + 6 ✓, (x + 3)(x - 2) = x² + x - 6 ✓, (x + 6)(x - 1) = x² + 5x - 6 ✓. The incorrect option (x - 3)(x + 4) = x² + x - 12, not x² - 7x + 12.
Find the product (x - 7)(x + 3).
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x² - 4x - 21
Using (x + a)(x + b) = x² + (a + b)x + ab with a = -7 and b = 3: (x - 7)(x + 3) = x² + (-7 + 3)x + (-7)(3) = x² - 4x - 21. The middle term coefficient is -7 + 3 = -4, and the constant term is (-7) × 3 = -21.
Which equation has roots x = 3 and x = -2?
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x² - x - 6 = 0
If x = 3 and x = -2 are roots, then (x - 3) = 0 and (x + 2) = 0. So the equation is (x - 3)(x + 2) = 0. Expanding: (x - 3)(x + 2) = x² + 2x - 3x - 6 = x² - x - 6 = 0.
Solve x² + 5x - 14 = 0.
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x = 2 or x = -7
Step 1: Find two numbers that add to 5 and multiply to -14. Consider factor pairs of 14: (1,14), (2,7). For -14: (7,-2) gives 7 + (-2) = 5 ✓. Step 2: x² + 5x - 14 = (x + 7)(x - 2). Step 3: (x + 7)(x - 2) = 0 gives x + 7 = 0 or x - 2 = 0. Step 4: x = -7 or x = 2.
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- 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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