ECAT Pre General Science Mathematics Chapter 6 Quadratic Equations Online Test

A polynomial P(x)has a factor (x-a)if P(a) =

• a A
• x B
• 1 C
• 0 D

There are ______ basic techniques for solving a quadratic equation

• Two A
• Three B
• Four C
• None of these D

The roots of ax2+bx+c=0 are

• Rational ⇔ b2 -4 ac ≥ 0 A
• Irrational ⇔ b2-4 ac > 0 B
• Real ⇔ b2-4 ac ≠ 0 C
• Rational⇔ b2-4 ac = 0 D

• Only one real solution A
• Exactly three real solution B
• Exactly one rational solution C
• Non-real roots D

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

• Vertex of parabola A
• Co-ordinates of parabola B
• Roots of the equation C
• Coefficient of the equation D

The two parts into which 57 should be divided so that their product is 782 are

• 43,14 A
• 34,23 B
• 33,24 C
• 44,13 D

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

• (-3,10) A
• (-3,-10) B
• (3,10) C
• (3,-10) D

If x³+ 4x³- 2x +5 is divided by x - 1, then the reminder is

• 8 A
• 6 B
• 4 C
• None of these D

Roots of the equation x²+ 5x - 1 = 0 are

• Rational A
• Irrational B
• Complex C
• None of these D

The solution of equation x2 + 2 = 0 in the set of real number is

• Infinite set A
• Singleton set B
• Null set C
• None of these D

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

• 
  A
• 
  B
• 
  C
• 
  D

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

• 0 A
• 2 B
• 18 C
• 14 D

If x-2 and x-1 both are factors of x³-3x³+2x-4p, then P must equal to

• 1 A
• 2 B
• 0 C
• -2 D

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is a factor of x³- 3x²+ 2x - 6

• x + 2 A
• x + 3 B
• x - 3 C
• x - 4 D

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

• 
  A
• 
  B
• 
  C
• 
  D

In quadratic equation, if the replacement of y with -y leaves the equation unchanged, then the graph is

• Straight line A
• Circle B
• Hyperbola C
• Symmetric w.r.t.0 D

If ax²+ bx + x = 0 is satisfied by every value of x, then

• b = 0, c = 0 A
• c = 0 B
• b = 0 C
• a = b = c = 0 D

The roots of the equation ax²+ bx + x = 0 are real and distinct if

• b²- 4ac <0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these D

The roots of the equation x2 +6x-7=0,are

• 1 A
• 2 B
• 1 and -7 C
• -7 D

Root of the equation 3^x-1+ 3^1-x= is

• 2 A
• 1 B
• 0 C
• -1 D

If ax + bx + c =0 is satisfied by every value of x,then

• b = 0,c = 0 A
• c = 0 B
• b = 0 C
• a = b = c = 0 D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• -1-w² B
• 
  C
• 
  D

The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in

• 
  A
• 
  B
• 
  C
• 
  D

Roots of the equation x²- x = 2 are

• {2, -1} A
• {1, 0} B
• {2, 1} C
• {-2, 1} D

• Reciprocal equation A
• Exponential equation B
• Radical equation C
• None of these D

If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

• a = 0 A
• b = 0 B
• c = 0 C
• None of these D

w⁴= ______

• 0 A
• 1 B
• w C
• w² D