Wednesday, 14 December 2016

Chapter 04: Quadratic Equations

1)                  x4 – 3x3 + 4x2 – 3x + 1 = 0 is called
a)                  Reciprocal equation     b)         Exponential equation c)         Radial equation                       d)        None of these
2)                  w11 =
a)                  0                      b)         1          c)         w                     d)         w2
3)                  2x2 + 5/x + 3 is a
a)                  Polynomial of degree 0           b)         Polynomial of degree 2
c)         Quadratic equation                 d)        None of these
4)                  If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is
a)                  x2 + Sx – P = 0                        b)         x2 – Sx + P = 0
c)         x2 – sx – P = 0                         d)         x2 + Sx + P = 0
5)                  Roots of the equation x2 + 5x – 1 = 0 are
a)                  Rational                                   b)         Irrational
c)         complex                                  d)        None of these
6)                  If one root of the equation x2 – 3x + a = 0 is 2 then
a)                  0                      b)         1          c)         2                      d)         3
7)                  If the roots of 3x2 + kx + 12 = 0 are equal then k =
a)                  36                    b)         6       c)         4                      d)         12
8)                  The roots of the equation will be irrational if b2 – 4ac is
a)                  Positive and perfect square  b)            Positive but not a perfect square
c)         Negative                                  d)         Zero
9)                  w28 + w38 = a)                  0                      b)         1          c)         w                     d)         –1
10)              (2 + w) (2 + w2) =
a)                  1                      b)         2          c)         3                      d)         0
11)              Two quadratic equations in which xy term is missing and the coefficients of x2 and y2 are equal, give a linear equation by
a)                  addition                                   b)         subtraction
c)         multiplication                          d)         division
12)              If x3 + ax2 – a2x – a3 is divided by x + a, then he remainder is
a)                  –a3                   b)         a3                     c)         2a3                   d)         0
13)              If x2 – 7x + a has remainder 1 when divided by x + 1, then a = a)                  –7                    b)         7                      c)         0                      d)         None of these
14)              If is complex cube root of unity then 3 =
a)                  0                      b)         1                      c)         2                    d)         -2
15)              If , are roots of 2x2 – 4x + 5 = 0 then ( + 1) ( + 1) =
a)                  11 / 2  b)         –11 / 2             c)         2 / 11  d)         –2 / 11
16)              If , are roots of 2x2 – 4x + 5 = 0 then 2 + 2 =
a)                  –1                    b)         0                      c)         2                      d)         1
17)              If , are roots of 2x2 – 4x + 5 = 0 then 2 + 2 =
a)                  1                      b)         –1                    c)         5                      d)         2

18)              The four fourth roots of unity are
a)                  0,1,,2           b)         1,–1, i, –i         c)         –2, 2, 2i, –2i d)            None of these
1)                  The quadratic equation with roots 2 –            3 . And 2 +      3 is  a)                  x2 – 4x + 1 = 0                        b)         x2 – 3x + 3 = 0
c)         x2 + 4x + 1 = 0                                    d)         x2 – 4x – 1 = 0
2)                  The roots of the equation x2 + 6x – 7 = 0, are
a)                  1                      b)         2                      c)         1 and –7          d)         –7
3)                  The largest degree of the terms in the poly-nomials is called
a)                  term of the polynomial                        b)         degree of a polynomial
c)         co-efficient                                          d)         monomial
4)                  The graph of the quadratic equation is
a)                  Straight line                                         b)         Circle
c)         Parabola                                              d)         Ellipse
5)                  Which of the following is a factor of P(x) = 2x3 + 3x2 – 3x-2?
a)                  x + 1    b)         2x + 1              c)         3x + 1              d)         2x – 1
6)                  (x – 1) is a factor of
a)                  2x3 – 3x2 + 9                            b)         2x2 + 5x – 8
c)         48x2 – 46x – 9                                     d)         x9 – 1
7)                  If the polynomial x3 + 4x2 – 2x + 5 is divided by x – 1, then the remainder is
a)                  1                      b)         –1                    c)         8                      d)         –8
8)                  The equation whose roots are 2, –3 and 7/5 is
a)                  5x3 – 2x3 – 37x + 42 = 0                     b)         2x2 + 3x + 7 = 0
c)         –3x2 + 2x + 7/5                                   d)         2x3 – 3x2 – 7x + 5 = 0
9)                  If x – 2 and x – 1 both are factors of x3 – 3x2 + 2x – 4p, then P must equal to
a)                  1                      b)         2                      c)         0                      d)         –2
10)              r what value of P is x2 – Px + P divisible of x – P?
a)                  1                      b)         –1                    c)         – ½                  d)         0
11)              If a polynomial P(x) is divided by x – c, then the remainder is
a)                  P(x)                  b)         x – c                c)         x                      d)         P(c)
12)              If f(x) = 3x2 + Px – 2, and f(–2) = 2, then P = 0
a)                  4                      b)         5                      c)         6                      d)         3
13)              Which of the following is not the factor of x4 – 13x2 + 36
a)                  x + 5    b)         (x – 2)              c)         (x + 2)             d)         x + 3
14)              When the Polynomial Px2 + 2x3 + qx + c, is divided by x + 1 and x – 2 the remainder remains same, then P + q =
a)                  3                      b)         –2                    c)         –6                    d)         6
15)              Each complex cube root of unity is square of
a)                  itself   b)         1                      c)         –1                    d)         the other
16)              If is the complex cube root of unit, then -12
a)                  1 /      b)                              c)         –1                    d)         1
17)              If is the complex root of unity, then (1 + - 2)3 – (1 - + w2)3
a)                  –12   b)         2                    c)         0                      d)         –1 19)              Sum of all the four fourth roots of unity is
a)                  i                       b)         –i                     b)         1                      d)         0
20)              The complex fourth roots of unity are
a)                  Additative inverse of each other                     b)         Conjugate of each other
c)         Multiplicative inverse of each other               d)         Reciprocals to each other
21)              Product of the complex cube roots of unit is equal to
a)                  i                       b)         –i                     c)         –1                    d)         1

19)              If the polynomial x3 + 4x2 – 2x + 5 is divided by x + 1, then the remainder is
a)                  4                      b)       6                      c)         8                      d)         10