Mathematics - Quadratic Equations

Question - 1

For the equation 3x2 + px + 3 = 0,p > 0; if one of the roots is square of the other,then p is equal to

  • A \(\frac{1}{2}\)
  • B 1
  • C 3
  • D \(\frac{ 2 }{ 3 }\)

Question - 2

If 1,a1,a2,a3,....an-1 are the nth roots of unity,then value of (1 - a1) (1 - a2)(1 - a3)...(1 - an-1),is

  • A n
  • B n2
  • C n3
  • D 0

Question - 3

The equation \(\sqrt { x+1 } \)- \(\sqrt { x-1 } \)  = \(\sqrt { 4x-1 } \), has

  • A no solution
  • B one solution
  • C two solutions
  • D more than two solutions

Question - 4

The number of the real roots of the equation |x2| + 3|x| + 2 = 0, is

  • A 4
  • B 3
  • C 2
  • D 0

Question - 5

If b > a,then the equation (x-a)(x-b)-1 = 0,has

  • A both roots in [a,b]
  • B both roots in (-\(\alpha\),a)
  • C both roots in (b,\(\infty\))
  • D one root in (- \(\infty\),a) and other in (b, \(\infty\))

Question - 6

Let \(\alpha,\beta\) be the roots of x2 - x + p = 0 and \(\gamma,\delta\) be roots of x2 - 4x + q.If \(\alpha,\beta,\gamma,\delta\) are in G.P., then the integral values of p and q respectively,are

  • A -2,-32
  • B -2,3
  • C -6,3
  • D -6,-32

Question - 7

The real roots of the equation 7log7(x2-4x+5) = x-1,are

  • A 1 and 2
  • B 2 and 3
  • C 3 and 4
  • D 4 and 5

Question - 8

If a,b,c are real numbers.such that a2+b2+c2 = 1,then ab +bc + ca lies in the interval

  • A \([\frac{1}{2},2]\)
  • B [-1,2]
  • C \([-\frac{1}{2},1]\)
  • D \([-{1},\frac{1}{2}]\)

Question - 9

If the roots of the equation x2 -2ax+a2+a-3 = 0 are real and less than 3,then

  • A a < 2
  • B  \(2 \le a \le 3\)
  • C \(3 < a \le 4\)
  • D a > 4

Question - 10

If \(\alpha\) and \(\beta\) (\(\alpha < \beta\)) are the roots of the equation x2 + bx + c = 0,where c < 0

  • A 0< \(\alpha\)< \(\beta\)
  • B \(\alpha\) <0< \(\beta\) <| \(\alpha\) |
  • C \(\alpha\) < \(\beta\) <0
  • D \(\alpha\)<0<| \(\alpha\)|< \(\beta\)
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