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Question 1 of 29
1. Question
If a polynomial p(y) is divided by y + 2, then which of the following can be the remainder:
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Question 2 of 29
2. Question
If a polynomial p(x) is divided by b – ax; the remainder is the value of p(x) at x =
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Question 3 of 29
3. Question
If the polynomials \(ax^{3} + 4x^{2} + 3x – 4\) and \(x^{3} – 4x + a\), leave the same remainder when divided by (x – 3), then value of a is :
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Question 4 of 29
4. Question
If p(x) = \(2x^{4} – ax^{3} + 4x^{2} + 2x + 1\) is a. multiple of 1 – 2x, then find the value of a :
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Question 5 of 29
5. Question
If 2 is a zero of p(x) = \((ax^{3} + bx^{2} + x – 6)\) and p(x) leaves a remainder 4 when divided by (x – 2), then the values of a and b are (respectively):
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Question 6 of 29
6. Question
If x101 + 1001 is divided by x + 1, then remainder is:
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Question 7 of 29
7. Question
If one zero of a polynomial p(x) = \(ax^{2}\) + bx + c(a ≠ 0) is zero, then, which of the following is correct:
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Question 8 of 29
8. Question
If α, s are the zeroes of \(x^{2}\) – lx + m, then \(\frac{α}{s}\) + \(\frac{s}{α}\)
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Question 9 of 29
9. Question
sum of the squares of the zeroes of the polynomial p(x) = \(x^{2}\) + 7x – k is 25, find k.
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Question 10 of 29
10. Question
If one zero of \(3x^{2} – 8x + 2k + 1\) is seven times the other, find k.
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Question 11 of 29
11. Question
Let, α, s, v be the zeroes of \(x^{3} + 4x^{2} + x 6\) such that product of two of the zeroes is 6. Find the third zero.
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Question 12 of 29
12. Question
If a, s are the zeroes of \(x^{2} – 8x + λ\), such that α – s = 2, then X =
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Question 13 of 29
13. Question
Find a and b so that the polynomial \(6x^{4} + 8x^{3} – 5x^{2} + ax + b\) is exactly divisible by \(2x^{2} – 5\).
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Question 14 of 29
14. Question
If α, s are the zeroes of p(x) = \(2x^{2} – 5x + 7\), write a polynomial with zeroes 2α+3s and 3α+2s.
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Question 15 of 29
15. Question
If sum of the two zeroes of a cubic polynomial x^{3} – \(ax^{2} + bx – c\), is zero, then which of the following is true:
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Question 16 of 29
16. Question
If a, s are the zeroes of p(x) = \(2x^{2} + 5x + k\) such that, \(α^{2}+ s^{2}+ αs\) = \(\frac{21}{4}\), then k equals,
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Question 17 of 29
17. Question
If α, s are the zeroes of \(x^{2} + px + q\), then a polynomial having zeroes \(\frac{1}{α}\) and \(\frac{1}{s}\) is,
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Question 18 of 29
18. Question
Find the number of zeros in the graph given:
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Question 19 of 29
19. Question
Write the zero of the polynomial p(x), whose graph is given :
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Question 20 of 29
20. Question
If α, s, v are the zeros of the polynomial \(2x^{3} – x^{2} + 3x 1\), find the value of (αsv) + (αs + sv + vα).
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Question 21 of 29
21. Question
If the zeros of the polynomial \(x^{3} – 3x^{2} + x +1\) are p – q,p and p + q. Find the value of q.
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Question 22 of 29
22. Question
A quadratic polynomial has :
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Question 23 of 29
23. Question
If α, s are the roots of cx^{2} – bx + a = 0 (c 0), then α + s is:
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Question 24 of 29
24. Question
If P(x) and D(r) are any two polynomials such that D(x) ≠ 0, there exists unique polynomial Q(x) and R(x) such that, P(x) = D(x). Q(x) + R(x) where :
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Question 25 of 29
25. Question
When we divide \(x^{3}\) + 5x + 7 by \(x^{4} – 7x^{2} – 6\) then quotient and remainder are (respectively):
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Question 26 of 29
26. Question
The value of b, for which \(2x^{3} + 9x^{2} – x – b\) is exactly divisible by 2x + 3 is:
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Question 27 of 29
27. Question
If α and s are two zeros of the polynomial p(x), then which of the following is a factor of p(x):
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Question 28 of 29
28. Question
Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and the product of its zeros as 2, +5, 3, respectively.
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Question 29 of 29
29. Question
Write a polynomial with zeros 1, – 1 and 1.
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