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

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

If 3x4 +4x3+x5is divided by x+1 , which of the following is the remainder

• 7 A
• -2 B
• 6 C
• 1 D

If a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is

• 8 A
• 12 B
• 10 C
• 14 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 0 A
• a³ B
• 2a³ C
• -2a³ D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

• 
  A
• 
  B
• 
  C
• 
  D

The graph of the quadratic equation is

• Straight line A
• Circle B
• Parabola C
• elipse D

Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

• α = β A
• αβ = 1 B
• α = β C
• α = 1 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

w⁷³= ______

• 0 A
• 1 B
• w C
• w² D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

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

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

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon 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 minimum value of the quadratic function f(x) = x2 +6x -2, is

• 11 A
• 6 B
• -11 C
• 13 D

Roots of the equation x²+ 7x + 12 = 0 are

• {3, -4} A
• {-3, 4} B
• {3, 4} C
• {-3, -4} D

The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

• 
  A
• 
  B
• 
  C
• 
  D

The roots of the equations will be equal if b²- 4ac is

• Positive A
• Negative B
• 1 C
• Zero D

The maximum value of the quadratic function f(x) = -2x2+20x,is

• 4 A
• 3 B
• 50 C
• 7 D

• 1 A
• -1 B
• 5 C
• 2 D

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

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

• 1 A
• 2 B
• 1 and -7 C
• -7 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

Roots of the equation x²- x = 2 are

• {2, -1} A
• {1, 0} B
• {2, 1} C
• {-2, 1} 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 x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

• -7 A
• 7 B
• 0 C
• None of these D

The sum of the roots of the equation x2 -6x +2 = 0 is

• -6 A
• 2 B
• -2 C
• 6 D

If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

• p²+ c/a A
• p²+ a/c B
• p²+ c/a C
• p²- c/a D