Polynomials - MCQ - Class -10

Polynomials

1.     1.   Fill in the blank

a)       A polynomial of degree 0 is called a ------------- polynomial.    (Constant)

b)      A polynomial of degree 1 is called a ------------ polynomial.     (linear)

c)       A polynomial of degree 2 is called a ------------ polynomial.     (Quadratic)

d)      A polynomial of degree 3 is called a ------------ polynomial.     (Cubic)

e)      A polynomial of degree 2 is called a ------------ polynomial.     (bi -Quadratic)

f)        The number of zeros of a quadratic polynomial is -----.            (2)

g)       The number of zeros of a cubic polynomial is -----.                    (3)

h)      The graph of a quadratic polynomial is a -----------. (Parabola)

i)        A quadratic equation can have ------------- two roots. (exactly/ at least / at most)  - at most

j)        If α is a zero of p(x) then ------------- is a factor of p(x)   { x – α )

                2.  if a, b, c are the zeros of the polynomials 2x³ – x² + 3x – 1, find the value of (abc) + (ab + bc + ca)                                                                                                                                                                 

a)       2                      b) 1.5                     c) ½                        d) 0

2           3. The value of p for which 2x³ + 9x² – x – p is exactly divisible by 2x + 3 is –

a)       – 15                b) 15                      c)9                          d) – 9

3     4.   If one of the zeros of the quadratic polynomial (k -1) x² + kx + 1 is – 3 , then the value of k is –

a)       4/3                 b) -4/3                  c) 2/3                    d) -2/3

4     5.   If P(x) and D(x) are two polynomials such that D(x) ≠ 0, there exist unique polynomials Q(x) and R(x) such that P(x) = D(x). Q(x) + R(x) where: -

a)       R(x) = 0 and deg R(x) > deg Q(x)

b)      R(x) = 0 or deg R(x) > deg Q(x)

c)       R(x) = 0 or deg R(x) < deg Q(x)

d)      R(x) = 0 and deg R(x) > deg Q(x)

5 6.  Write a polynomial with the sum, sum of product of its zeros taken two at a time and the product of its zeros as -2, +5 and – 3 respectively.

a)       2x³ + 3x² – 5x + 3                      

 b) 4x³ + 7x² – 5x + 3                                                                               

c) x³ + 2x² + 5x + 3                       

 d) 2x³ - 3x² + 7x + 3

6.     If 2 + sqr root 3 and 2 - sqr root 3 are  the two zeros of a polynomials then which of the polynomial you can make with these roots?

a)       x² – 4x + 1                                    b) x² + 4x + 1

c) 4x² – 4x + 3                                     d) x² – 4x + 3

7.  If one zero of the polynomial ax³ + bx² + cx + d is zero, then the product of other two zeros is –

                a) a                         b) b/a                    c) -c/a                   d) d/a

8  If the polynomials ax³ + 4x² + 3x – 4 and x² – 4x + a, leave the same remainder when divided by           x -3, then value of a is –

                a) 20                      b) -1                       c) 1                         d) -2b

Dr Rajesh Kumar Thakur