IX Math Ch Polynomials Questions1

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  • Q1. Find the zeroes of the polynomial p(x) =2x-5.

    Q2. Check whether -2 and 2 are the zeroes of the polynomial x3 - 8

    Q3. Evaluate (497 X 503)

    Q4. Without actual division find the remainder, when the polynomial

    1

    2

    x +

    Q5. Without calculating cubes, find the value of (-12)3 + (7)3 + (5)3.

    Q6. If x2+ px + q = (x + a)(x + b) , then factorise x2 + pxy + qy2

    Q7. Factorise: 2y3 + y2 - 2y -1

    Q8. What are the possible expressions for the dimensions of the cuboids

    whose volume is given by3 2 x 3x 9x 5

    09.

    10.

    If x=1 is a zero of a polynomial f(x) = x3-2x2+4x+k. Write the value of k

    For what value of k , -4 is a zero of the p(x)=. x2 x - (2k+2) ?

    11. Verify whether 3 and 2 are the zeros of the poly. (x - 2)(x -3)?

    12.

    13

    Find the zeros of the polynomial f(x) =4x2+8x

    Find a quadratic polynomial each with the given zeros as sum and the product of its zeros

    respectively (a) , -1 (b) 2 , 1/3

    4x3 - 3x2 + 2x - 4 is divided by

  • 14. Using division algorithm, find the quotient and the remainder on dividing f(x) by g(x) , where

    f(x) =6x3 +13x2 + x - 2 and g(x) =2x+1

    15 If , are the zeros of 2y2+7y+5 write the value of + + .

    16 Find the zeros of a quadratic polynomial 5x2-4-8x and verify the relationship between the zeros and

    the coefficients of the polynomial.

    17 If , are the zeros of the poly. f(x)=x2-px+q, find the value of

    (a) 2+2 (b)1/ +1

    18 On dividing x3+2x2-5x-6 by a polynomial g(x) the quotient and remainder were x+1 and - 4x -4

    respectively Find the polynomial g(x)

    19 If (x + a) is a factor of 2x2+2ax+5x+10. Find a.

    20 Find all the zeros of 2x4-9x3+5x2+3x-1, if two of its zeros are 2+3 & 2- 3

    21 If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1, the remainder comes out to be (ax + b), find a and b.

    22

    23

    Find all other zeroes of the polynomial p(x) = 2x3 + 3x2 11x 6, if one of its zero is 3.

    24 If one of the zeroes of the quadratic polynomial (k1) x2 + k x + 1 is 3, then the value of k is(A) 4/3 (B) 43 (C) 2/3 (D) 2/3

    25 A quadratic polynomial, whose zeroes are 3 and 4, is

    (A) X2 x + 12 (B) x2 + x + 12 (C) x2/2 x/2 -6 (D) 2x2 + 2x 24

    26 If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and 3, then

    (A) a = 7, b = 1 (B) a = 5, b = 1 (C) a = 2, b = 6 (D) a = 0, b = 6

    27 The number of polynomials having zeroes as 2 and 5 is

    (A) 1 (B) 2 (C) 3 (D) more than 3

    28

    If one of the zeroes of the cubic polynomial x3 + ax2 + b x + c is 1, then the product of the

    other two zeroes is

    (A) b a + 1 (B) b a 1 (C) a b + 1 (D) a b 1

    If one zero of the polynomial (a2 +9)x2 +13x +6a is reciprocal of the other . Find the value of a.

  • 29 Find the zeroes of the polynomial x2 +1/6x 2, and verify the relation between the coefficients

    and the zeroes of the polynomial

    30 Find the zeroes of the following polynomials by factorization method and verify the relations

    between the zeroes and the coefficients of the polynomials 2s2 (1 + 2 2) s + 2

    31 Find a quadratic polynomial, the sum and product of whose zeroes are 2 and 3/2,

    respectively. Also find its zeroes

    32 If the remainder on division of x3 + 2x2 + k x +3 by x 3 is 21, find the quotient and the value of

    k. Hence, find the zeroes of the cubic polynomial x3 + 2x2 + k x 18

    33 Given that 2 is a zero of the cubic polynomial 6x3 + 2 x2 10x 4 2 , find its other two

    zeroes.

    34 Given that x 5 is a factor of the cubic polynomial x3 35x2 + 13x 3 5, find all the zeroes

    of the polynomial.

    35 For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5 x4 4x3 + 3x2 + 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?

    36 The zeroes of the quadratic polynomial x2 + 99x + 127 are

    (A) both positive (B) both negative (C) one positive and one negative (D) both equal

    37 The zeroes of the quadratic polynomial x2 + k x + k, k 0,

    (A) cannot both be positive (B) cannot both be negative (C) are always unequal (D) are always equal

    38 If the zeroes of the quadratic polynomial ax2 + bx + c, c 0 are equal, then(A) c and a have opposite signs (B) c and b have opposite signs (C) c and a have the same sign (D) c and b have

    the same sign

    39 If one of the zeroes of a quadratic polynomial of the form x2+ax + b is the negative of the other, then it

    (A) has no linear term and the constant term is negative.

    (B) has no linear term and the constant term is positive.

    (C) can have a linear term but the constant term is negative.

    (D) can have a linear term but the constant term is positive.

    40 The number of polynomials having zeroes as 2 and 5 is

    (A) 1 (B) 2 (C) 3 (D) more than 3

    41 Find the zeroes of 2x3 11x

    2 + 17x 6.

    42 Find the quadratic polynomial, the sum and the product of whose zeroes are 1/2, and 2 .

    43 Find the values of m and n for which x = 2 and 3 are zeroes of the polynomial: 3x2 2mx + 2n.

    44 Check whether x2 + 4 is factor of x

    4 + 9x

    2 + 20

  • 45 Divide the polynomial (x4 + 1) by (x 1) and verify the division algorithm.

    46 Find all zeroes of x4 3x3 5x2 + 21x 14, if two of its zeroes are 7 and 7

    47 On dividing x3 3x

    2 + x + 2 by a polynomial g(x), the quotient and remainder were x 2 and 2x + 4

    respectively, find g(x).

    48 Given that 2 is a zero of the cubic polynomial 6x3 + 2 x2 10x 4 2 , find its other two zeroes.

    49 Find k so that x2 + 2x + k is a factor of 2x4 + x3 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.

    50 Given that x 5 is a factor of the cubic polynomial x3 3 5x

    2 + 13x 3 5 , find all the zeroes of the

    polynomial.

    51 Find a quadratic polynomial, the sum and product of whose zeroes are 0 and 5 respectively.

    52 Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively

    53 If a and b are the zeros of the quadratic polynomial f(x)= x2-5x+4, find the value of 1/a + 1/b- 2ab

    54 Find the zeroes of the quadratic polynomial 4 3 x2 + 5 x - 2 3 and verify the relationship

    between the zeroes and the coefficients.

    55 Find the zeroes of the quadratic polynomial 4u2 + 8u and verify the relationship between the

    zeroes and the coefficients

    56. Find the quadratic polynomial, the sum and product of whose zeroes are 2 and 3 respectively.

    57. If a and b are the zeros of the given quadratic polynomial f(x)= 5x2 - 7x + 1, find the value 1/a + 1/b

    58. Find the zeroes of the polynomial x2 3 and verify the relationship between the zeroes and the

    Coefficients

    59. Find the remainder when p(x)= x3-6x2+2x-4 when divided by 1 - 2x.

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