OBJECTIVES OF POLYNOMIAL, CLASS: IX

POLYNOMIAL

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FATHER OF MODERN MATHEMATICS RENE DESCARTES


FILL IN THE BLANKS


1.The word polynomial comes from ________________
2.The word polynomial was introduced in latin by _______________________
3.Polynomial with one term is known as_______________
4.Polynomial with two term is known as_______________
5.Polynomial with three term is known as______________
6.Polynomial with four term is known as_______________
7.Polynomial with five term is known as _______________
8.Polynomial of degree 1 is known as _________________
9.Polynomial of degree 2 is known as _________________
10.Polynomial of degree 3 is known as _________________
11.Polynomial of degree 4 is known as ___________________ polynomial
12.Polynomial of degree 5 is known as ___________________ polynomial
13.________________  in 1637 introduced the graph of a polynomial equation
14.If the leading coefficient of a univariate polynomial is one , then it is called ______________
15.A polynomial in one variable is called a ___________________polynomial
16.When P(x) is divided by ( x – a), then P(a)represents ________________
17.If P(c) =  0, then ( x - c ) is a __________ of P(x)
18.X^3 + Y^3 + Z^3 = _________ ,if X + Y + Z is zero.
19.X^3 + Y^3 +Z^3 – 3XYZ = K(X+Y+Z){(X-Y)^2 + (Y-Z)^2 + (Z-X)^2}, then k = _______
20.Every ____________ polynomial has zero.
21.The degree of zero polynomial is __________________
22.The value of 3y^3 – 4y + √11 at y = 2 is _______________
23.If x + y = 4 and xy = 6, then the value of x^3 + y^3 = _______
24.A constant polynomial have  _____________ zero
25.A quadratic polynomial have almost _______ zeros
26.A polynomial of degree n have almost ___________ zeroes
27.A constant polynomial zero is known as ___________ polynomial
28.A zero polynomial have ______________ zeros
29.Every real number is a zero/es of the ________ polynomial
30.A zero of a polynomial ______________ be zero
31.A polynomial can have more than _______ zero
32.Every linear polynomial has _______ and only _______ zero
33.Exponent of every polynomial is _______________ number
34.Degree of x^2 + 3x^4 + 66 is _________________
35.Degree of x^2y^2 + x^3y^2 – 2x^3 is ______________
36.Remainder theorem is also known as ___________

TRUE OR FALSE

1.A polynomial have more than one zero.
2.The zero of the polynomial p(x) = 2x – 1 is ½.
3.The remainder when p(x) = 2x^3 – 2x^2 + x – 1 is divided by x + 1 is -12.
4.( x + 1) and ( 2x – 3) are factor of polynomial 2x^2 – 9x + 12.
5.2x+ √2is polynomial.
6.X^2 – x^1/2 is polynomial.
7.Y^2 – 1/y - 2 is polynomial.
8.Is x^4 + 4 = (a^2 + a + 2)(a^2 – a + 2) ?
9.Quadratic polynomial is univariate
10.x^2 + x^3 – 4x^4 is monic.

MULTIPLE CHOICE QUESTIONS

1.  Which one is not a polynomial
      (a)   4x^2 + 2x – 1(b)   y + 3/y(c)   x^3 – 1(d)   y^2 + 5y + 1

2.  The polynomial ax^2 + bx + cx^4 + 5 is 
      (a)   linear           (b) quadratic          (c) cubic            (d)  Biquadratic

3.  Identify the polynomial
      (a)   x^–2 + x^–1 + 5     b) x^1/2 -1/2    (c)  1/x  + (- x)  (d)   3x^2 + 7

4.  The zero of the polynomial p(x) = 2x + 5 is
      (a)   2        (b)   5      (c)   2/5        (d)   -5/2

5.  The number of zeros of x^2 + 4x + 2
      (a)   1      (b)   2      (c)   3      (d)   none of these

6.  The polynomial of type px^2 + qx + r, a = 0 is of type
      (a)   linear      (b)   quadratic     (c)   cubic       (d)   Biquadratic

7.  The value of k, if (x – 1) is a factor of 4x^3 + 3x^2 – 4x + k, is
      (a)   1     (b)   2      (c)   –3       (d)   3

8.  The degree of polynomial p(x) = x+√(x^2+1)  is
      (a)   0     (b)   2      (c)   1       (d)   3

9.  If 3 + 6 – 9 = 0, then the value of (3)3 + (6)3 – (9)3 is
      (a)   260       (b)  –360        (c)  –486   (d)   486

10.  If value of 104 × 96 is
      (a)   9984   (b)   9469      (c)   10234     (d)   11324

11.  The value of 5.63 × 5.63 + 11.26 × 2.37 + 2.37 × 2.37 is
      (a)   237      (b)   126     (c)   56        (d)   64

12.  The value of [(361)^3 (+139)^3)]/[(361)^2-361*139+(139)^2 ] is
      (a)   300  (b)   500   (c)   400     (d)   600

13.  If x + y = 2, x^2 + y^2 = 5 then xy is
      (a)   1    (b)   3      (c)   2       (d)  None of these


14.  If x + 2 is a factor of x^3 – 2ax^2 + 16, then value of a is
      (a)   3    (b)   1    (c)   4   (d)   2

15.  If one of the factor of x^2 + x – 20 is (x - 4). Find the other
      (a)   x – 4   (b)   x + 2      (c)   x + 5        (d)   x – 5

16. which one of the following algebraic expressions is a polynomial in variable x ?
(a)  x2 + 1/x^2             (b) √x+1⁄(√x)               (c) x^2+ (3x)^(3⁄2)/√x    (d) none of these

17. Degree of the polynomial p(x) = ( x + 2 )( x – 2 ) is 
(a) not define            (b) 1                             (c) 0                         (d) 2 

18. If x^3 + y^3 + z^3 = 2k[ ( x – y)^2 + ( y – z)^2 + ( z – x)^2 ] then k is
(a) 1/4                         (b) 1/2                          (c) any real number      (d) not define

19. If both x = 2 and x = ½ are factors of px^2 + 5x + r, then p = 
(a) ¾ r                       (b) 2r                           (c) r/2                         (d) r 

20. Who is the father of polynomials ?
(a) Diophantus           (b) Newton                  (c) Euclid                      (d) Aryabhatta


MATCH THE FOLLOWING

Match or Choices for the correct combination of elements from List-A and list – B are given as options (a), (b), (c) & (d) out of which one is correct.

1. List- B shows the degree of polynomials given in List- A.

                                                                
          List-A                                       List- B

p) 2 – y^2 – y^3 + 2y^8                1) 2
q) 2                                                2) 1
r) 5X - √7                                      3) 0
s) 4 – X^2                                      4) 8         


CODE
                p q r s
            a) 1 3 2 4
            b) 4 3 2 1
            c) 4 2 3 1
            d) 2 3 4 1



2. List – B gives the values of k for polynomials given in List-B when it divided by x – 1


             LIST-A                                LIST – B
p) Kx2 – 3x – 2k                        1)  0
q) X^2 – x + k                            2) -3
r) 2x^2 + kx + 3                      3) (√2-1)/3
s) 3kx^2 - √2x + 1                     4)  -5

CODE
p q r s
a) 2 1 4 3
b) 4 1 3 2
c) 1 4 3 2
d) 2 2 4 1
3. List-B gives value of the polynomials given in List – A at the given points.


            LIST-A                                      LIST-B
p) 3t^3 – 2t^2 + t at t = ½                    1) 2
q) 3x^3 + x^2 – 20x +12 at x = 2/3     2) -1
r) 7u^5-4u^3 + 2 at u = 0                    3) 3/8
s) (3s – 1)(2s-3) at s = 1/2                   4) 0





CODE
    p q r s
a) 1 2 3 4
b) 4 2 1 3
c) 4 3 2 1
d) 3 4 1 2




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