Download polynomial class 10 test paper

Cynesure Institute
POLYNOMIAL
Class 10
POLYNOMIAL
CLASS 10
1. A quadratic polynomial whose product and sum of zeroes are 1/5 and 3 respectively.
3x2 – 32x +1.
2. Check if x2 + 4 is factor of x4 + 9x2 + 20.
3. Find a and b if the zeroes of q(x) = x3 + 2x2 + a are also the zeroes of the polynomial p(x)
= x5 – x4 – 4x3 + 3x2 + 3x + b?
4. Find a quadratic polynomial, the sum and product of whose zeroes are √2 and – 3/2
respectively.
1
5. Find a quadratic polynomial, the sum and the product of whose zeroes are and –2
2
respectively.
6. Find all the three zeroes of 2x3 – 11x2 + 17x – 6.
7. Find k if one zero of the quadratic polynomial x2 + 3x + k is 2.
8. Find the value of k for which - 4 is zero of the polynomial x2 – x – (2k+2)? 9
9. Find the value of k such that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Then find
all the zeroes of the two polynomials.
10. Find the zeroes of the polynomial 2x2 - 3x - 2.
11. Find the zeroes of the polynomials 2x2 – (1 + 2√ 2)x + √2and verify the relations
between the zeroes and the coefficients of the polynomials.
12. Find the zeroes of the polynomials 4x2 + 5 √2x – 3 and verify the relations between the
zeroes and the coefficients of the polynomials.
2
y – and verify the relations between the
3
3
zeroes and the coefficients of the polynomials.
13. Find the zeroes of the polynomials 7y2 –
11
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14. Find the zeroes of the polynomials y2 +
2
√5y – 5 and verify the relations between the
3
zeroes and the coefficients of the polynomials.
15. Find the zeroes of the quadratic polynomial 2x2 - 9 - 3x and verify the relationship
between the zeroes and the coefficients. Ans: 3, -3/2
16. For what values of m and n are x = 2 and –3 zeroes of the polynomial: 3x2 – 2mx + 2n.
17. Form a quadratic polynomial, the sum and product of whose zeroes are 3 and -2. x2-3x-2
18. Form the polynomial whose zeroes are 2 +3 and 2 - 3. Ans:p(x)=x2-4x+1
19. How many polynomials can have zeroes –2 and 5?
2
20. If ,  are zeroes of p(x)=kx2+4x+4 such that 2 +2=24, find k. Ans: k=3 or k= -1
21. If ,  are zeroes of the polynomial x2-2x-15, then find a quadratic polynomial whose
zeroes are 2 and 2. Ans: x2-4x-60
22. If ,  are zeroes of the quadratic polynomial ax2+bx+c, then find
 
(a) +
 
(b) 2 +2
(c) 2 - 2
(d) 3 +3
23. If √2 is a zero of the cubic polynomial 6x3 + √2 x2 – 10x – 4√2, find its other two zeroes.
24. If 1 is a zero of p(x) = ax2 -3(a-1)x -1, find the value of a. 1
25. If 2 is a zero of the cubic polynomial 6x3 + 2 x2 – 10x – 4 √2 , find other two zeroes.
26. If one zero of p(x) = (k–1) x2 + k x + 1 is (–3), find k.
27. If one zero of the cubic polynomial p(x)= x3 + ax2 + bx + c is (–1), find the product of
the other two zeroes.
28. If the square of difference of the zeroes of p(x)=x2+px+45 is144, find the value of p.
29. If two zeroes of the cubic polynomial ax3 + bx2 + cx + d are 0, find the third zero.
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30. If x – √5 is a factor of the cubic polynomial x3 – 3√ 5 x2 + 13x – 3√5 , find all the zeroes
of the polynomial.
31. If zeroes of the cubic polynomial x3 – 6x2 + 3x + 10 are a, a + b, a + 2b, find the values of
a and b.
32. If zeros of quadratic polynomial x2 + (a + 1) x + b are –3 and 2, find a and b.
33. If α and β . are zeroes of the polynomial 2x2 + 7x - 3, find the value of α2 + β2 . 61/4
34. It is given that 2 is a zero of both the polynomials 3x2+ax-14 and 2x3+bx2+x-2, then find
the value of 2-2b. 9
35. What are the sign of the zeroes of the quadratic polynomial x2 + 99x + 127?
36. If P(x)= 2x2-3x+5,3x+5, find p(-2).
37. Find the zeroes of P(x) = x2-2x-3.
38. If a and b are the zeros of 2x2+5x-10, find ab and a+ b.
39. Find the value of ‘k’ such that the quadratic polynomial x2-(k+6) x+2(2k+1) has sum of
the zeros is half of their product.
40. If a and b are the zeroes of the quadratic polynomial p(x) = x2-p(x+1)-c, show that (a +1)
(b +1)=1-c.
41. If the sum of the zeroes of the quadratic polynomial p(t) = kt2+2t+3k is equal to their
product, find the value of k.
42. Find the zeroes of P(x) = 2x2+9x-35.
43. Form the quadratic polynomial whore zeros are 3 and -5.
44. If a and b are the zeros of the quadratic polynomial p(x) = x2-px+q, find a2 + b2.
45. Find k so that the zeroes of the quadratic polynomial 3x2-kx+14 are in the ratio 7:6.
46. If a zero of the quadratic polynomial p(x) = 4x2-8kx-9 is negative of the other zero, find
the value of k.
47. If a and b are the zeros of the polynomial f(x) = x2+px+q form polynomial whore zeros
are (a + b )2 and (a - b )2.
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1. Find the remaining zeroes of the polynomial 2x3 + x2 - 6x - 3, if two of its zeroes are -3
and 3. x=-1/2
2. Find the remaining zeroes of the polynomial p(x)=2x4 +7x3-19x2-14x +30 if two of its
zeroes are 2 and -2. Ans: 3/2 and -5
3. Find the remaining zeroes of x4 – 3x3 – 5x2 + 21x – 14 if two of its zeroes are √7 and –
√7.
4. Divide the polynomial (x4 + 1) by (x – 1). Also verify the division algorithm.
5. 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).
6. Find p if the polynomial 6x3+16x2+px -5 is exactly divisible by 3x+5. 7
7. If p(x) = x4+2x3+8x2+12x+18 is divided by x2+5, the remainder comes out to be px+q.
Find p and q. p=2,q=3
8. Divide 30x4 +11x3-82x2-12x-48 by (3x2 +2x-4).
9. Obtain the remaining zeroes of 3x4 -15x3+13x2+25x-30, if two of its zeroes are
5
3
5
3
and -
. 2, 3
10. What must be added to 6x5+5x4+11x3-3x2+x+5 so that it may be exactly divisible by 3x22x+4?
11. Check if x – 1 can be the remainder on division of a polynomial by 2x + 3?
12. Find quotient and remainder on division of ax2 + bx + c by px3 + qx2 + rx + s?
13. If p (x) is divided by a polynomial g (x), the quotient is zero, what is the relation between
p (x) and g (x)?
14. If remainder when x3 + 2x2 + kx +3 is divided by x – 3 is 21, find the quotient and the
value of k.
15. Divide x4-5x+6 by 1- x2.
16. Cheek whether the polynomial t2-3 is a factor of the polynomial 2t4+3t3-2t2-9t-12 .
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