POLOYNOMIALS (X)
1. Show that x2 – 3 is a factor of 2x4
+ 3x3 -2x2 -9x – 12
2. Divide: 4x3
+ 2x2 + 5x - 6 by 2x2 + 3x + 1
3. Find other zeroes
of the polynomial p(x) = 2x4 + 7x3 – 19x2 –
14x + 30 if two of its zeroes are √2 and -√2
4. Find all the zeroes of the polynomial 3x4 + 6x3
- 2x2 – 10x – 5, if two of its zeroes are √5/3 and -√5/3
5. Find all the zeroes of 2x4 – 3x3 –
3x2 + 6x – 2, if it is known that two of its zeroes are √2 and -√2
6. Find all the zeroes of 2x4 - 9x3 +
5x2 +3x – 1, if two of its zeroes are 2 + √3 and 2 - √3
7. Find all the zeroes of polynomial 4x4 – 20x3
+ 23x2 + 5x – 6 if two of its zeroes are 2 and 3
8. If the polynomial f(x) = x4 -
6x3 +16x2 - 25x + 10, is divided by another polynomial x2
- 2x + k the remainder
Comes out to be x + a, find k and a
9. On dividing x3 – 3x2+ x + 2 by a
polynomial g(x), the quotient and remainder were x – 2 and -2x +4, respectively
Find g(x)
10. If the polynomial 6x4 + 8x3 – 5x2
+ ax + b is exactly divisible by the polynomial 2x2 – 5, then find
the values of
a and b
11. Find the values of m and n so that x4 + mx3
+ nx2 – 3x + n is divisible by x2 – 1
12. What must be subtracted from 2x4 – 11x3
+ 29 x2 – 40x + 29, so that the resulting polynomial is exactly
divisible
By x2-3x
+ 4
13. Find the polynomial, whose zeroes are 2 + √3 and 2 -
√3
14.Form a quadratic polynomial, one of whose
zero is 2 + √5 and the sum of zeroes is 4
15. If α and β are zeroes of the polynomial x2 –
2x – 15, then form a quadratic polynomial whose zeroes are 2α and 2β
16.Write
a quadratic polynomial, the sum and product of whose zeroes are 3 and -2
17. Find the zeroes of the polynomial and verify the
relationship between the zeroes and the coefficient
a) 4x2 – 4x + 1 b) x2
– 3 c) √3x2 – 8x + 4√3
18. If α and β are the zeroes of the polynomial 2y2
+ 7y + 5, write the value of α +β + αβ
19. If one root of the polynomial 5x3 + 13x + k is
reciprocal of the other, then find the value of k?
20. If one zero of the polynomial (a2 + 9) x2
+13x + 6a is reciprocal of the other. Find the value of a
21. If the zeroes of the polynomial x3 – 3x2
+ x+1 are a – b, a, a + b, find a and b
22. If α and β are the
zeroes of the polynomial f(x) = 6x2 + x -2, find the value of 1
+ 1 -
αβ
α β
23.If α and β are the
zeroes of the quadratic polynomial 2x2 + 3x - 5, find the value
of 1 +
1
α β
24. If α and β are the zeroes of the polynomial f(x) = x2
– 5x + k such that α – β = 1, find k
25. If α, β are the zeroes of a polynomial, such that α + β =
6 and α β = 4, then writes the polynomial
26. If the product of zeroes of the polynomial ax2
– 6x – 6 is 4, find the value of a
27.If α, β are the zeroes of quadratic polynomial 2x2
+ 5x + k, find the value of k such that (α + β)2 – α β = 24
28. If α and β are zeroes of x2 + 5x + 5, find the
value of α-1 + β-1
29. α, β are the zeroes of the quadratic polynomial x2
– (k+6)x +2 (2k – 1). Find the value of k if α + β = ½ α β
30. if α, β are the zeroes of the quadratic polynomial x2
– 7x + 10, find the value of α3 + β3
31. Find the sum and the product of the zeroes of cubic
polynomial 2x3 -5x2 – 14x + 8
32. Find the sum and product of the zeroes of quadratic
polynomial x2 – 3
33. If 1 is a zero of polynomial ax2 – 3(a-1) -1,
then find the value of a
34. If α, β are zeroes of quadratic polynomial x2
– (k + 6)x + 2(2k-1).Find k if α + β = 1/2αβ
35. Divide (6 + 19x + x2 – 6x3) by (2
+5x – 3x2) and verify the division algorithm
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