1. Sum of zeros of 3x² − 6x + 2.
- A2
- B−2
- C
- D−6
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Answer: A) 2
Sum = −b/a = −(−6)/3 = 2.
Class 10 Polynomials — practice questions with answers
Algebra — Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. If α and β are zeros of x² − 7x + 10, find 1/α + 1/β.
- A
- B
- C
- D
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Answer: A)
.
3. If one zero of x² + 7x + k is −2, find the other zero.
- A-10
- B-4
- C-6
- D-5
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Answer: D) -5
Sum of zeros = −b/a = −7. Other = −7 − (−2) = −5.
4. If the product of the zeroes of (k − 3)x² + 4x + 5 is 1, find k.
- A5
- B8
- C−2
- D3
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Answer: B) 8
Product of zeroes = . Setting gives k − 3 = 5, so k = 8. Answering −2 solves k − 3 = −5; 5 treats the leading coefficient as k instead of k − 3; and k = 3 would make the x² term vanish, so the expression would not even be a quadratic.
5. When 2x³ − 3x² + ax − 8 is divided by (x + 1), the remainder is −6. Find a.
- A7
- B−7
- C3
- D−13
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Answer: B) −7
By the Remainder Theorem the remainder is p(−1) = 2(−1)³ − 3(−1)² + a(−1) − 8 = −2 − 3 − a − 8 = −13 − a. Setting −13 − a = −6 gives a = −7. Check: 2x³ − 3x² − 7x − 8 at x = −1 gives −2 − 3 + 7 − 8 = −6 ✓. Substituting x = +1 instead of x = −1 gives a = 3; treating a(−1) as +a gives a = 7.
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