ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 6 (Quadratic Equations)

• 
  A
• 
  B
• 
  C
• 
  D

The roots of the equation will be irrational if b²- 4ac is

• Positive and perfect square A
• Positive but not a perfect square B
• Negative C
• Zero D

The roots of ax2 + bx + c = 0 are always unequal if

• b2 - 4ac = 0 A
• b2- 4ac ≠ 0 B
• b2- 4ac > 0 C
• b2- 4ac ≥ 0 D

The product of cube roots of unity is

• Zero A
• 1 B
• -1 C
• None of these D

A quadratic equation in x is an equation that can be witten in the form

• ax² + b = 0 A
• ax³ +b²+c=0 B
• ax² +bx+c=0 C
• ax³ +bx³+cx=0 D

• 
  A
• 
  B
• 
  C
• 
  D

In quadratic equation y=ax³ +bx+c, if b and c are both zero then the graph is

• Symmetric w.r.t.y-axis A
• Symmetric w.r.t.x-axis B
• Straight Line C
• Circle D

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

• k=0 A
• k=1 B
• k=w C
• k=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 product of the four fourth roots of unity is

• 0 A
• 1 B
• -1 C
• None of these D

• 0 A
• 1 B
• 2 C
• None of these D

If x³+ ax²- a²x - a³is divided by x + a, then the remainder is

• 0 A
• a³ B
• 2a³ C
• -2a³ D

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

x⁴- 3x³+ 3x + 1 = 0 is called ______

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

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

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

• (0, 2π) A
• (-π, -0) B
• (0,π) C
• None of these D

w⁷³= ______

• 0 A
• 1 B
• w C
• w² D

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D

Let the equation ax²- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

• (5, 3, 1) A
• (4, 3, 2) B
• (5, 5, 1) C
• (6, 4, 1) D

Roots of the equation x²- x = 2 are

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

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

• (x + 2)2(x - 1) A
• (x + 2)(x - 1)2 B
• (x+2)(x2- x- 2) C
• (x + 2)2(x - 1)2 D

If b²- 4ac is positive then the roots of the equation are

• Real A
• Imaginary B
• Positive C
• Negative 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

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

(x-1) is a factor of

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

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

• 2, 8 A
• 1, 3 B
• 1, 8 C
• 2, 3 D

• 0 A
• -1-w² B
• 
  C
• 
  D