ECAT Mathematics Chapter 6 Quadratic Equations Online Test

The roots of the equation ax²+ bx + c = 0 are complex/imaginary if

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

If a > 0, b > 0, c > 0, then the roots of the equation ax²+ bx + c = 0 are

• Real and negative A
• Non-real with negative real parts B
• Real and positive C
• Nothing can be said D

If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

• 0 A
• ±1 B
• ±5 C
• ±7 D

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

• Opens up A
• Opens down B
• close up C
• symmetric w.r.t.x.axis D

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

Another name of quadratic equation is

• Polynomial A
• 2nd degree polynomial B
• Linear equation C
• simaltaneous equations D

Both the roots of the equation (x - b) (x - c) + (x - c)(x - a) + (x - a)(x - b) = 0 are always

• Positive A
• Negative B
• Real C
• None of these D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

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

• 0 A
• 1 B
• 2 C
• 3 D

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

• 1 A
• 2 B
• 1 and -7 C
• -7 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

If x² + px + 1 is a factor of ax³+ bx +c, then

• a²+ c²= -ab A
• a²- c²= -ab B
• a²- c²= ab C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

The minimum value of the quadratic function f(x) = x2 +6x -2, is

• 11 A
• 6 B
• -11 C
• 13 D

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

• Rational A
• Irrational B
• Non-real C
• Zero D

There are ______ basic techniques for solving a quadratic equation

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

Roots of the equation 2x²- 7x + 3 = 0 are

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

A quadratic equation has two

• roots A
• degree B
• variables C
• constants D

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

• 8 A
• -16 B
• -64 C
• 16 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

w^-1= ______

• 0 A
• 1 B
• w C
• w² D

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

• Positive A
• Negative B
• Real C
• None of these D

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are

• 6, 10 A
• -6, -10 B
• 8, 8 C
• -8, -8 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

• 
  A
• 
  B
• 
  C
• 
  D

(x-1) is a factor of

• 2x³-3x²+9 A
• 2x³-5x-8 B
• 48x^2-46x-9 C
• x⁹-1 D