POLYNOMIAL
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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