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

Roots of the equation 9x²- 12x + 4 = 0 are

• Real and equal A
• Real and distinct B
• Complex C
• None of these D

• 1 A
• 2 B
• 0 C
• 4 D

The graph of the quadratic equation is

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

• -1 A
• 0 B
• 2 C
• 1 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

Find a if 1 is a root of the equation x²+ ax + 2 = 0

• 3 A
• -3 B
• 2 C
• 0 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

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

If the roots of 3x2+kx + 12 = 0 are equal then k = ______

• 
  A
• 
  B
• 
  C
• 
  D

If x⁴- 10x²- 2x + 4 is divided by x + 3, then the reminder is

• 1 A
• 0 B
• 4 C
• None of these D

Roots of the equation x²- x = 2 are

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

• Lies between 4 and 7 A
• Lies between 5 and 9 B
• Has no value between 4 and 7 C
• Has no value between 5 and 9 D

The standard parabolic form of the equation f(x) = x² +4 x +1 is

• x(x+4)+1 A
• (x+2)²-3 B
• (x+4)³ + 9 C
• x(x-2)²+1 D

• 
  A
• 
  B
• 
  C
• 
  D

w¹¹= ______

• 0 A
• 1 B
• w C
• w² D

w^-1= ______

• 0 A
• 1 B
• w C
• w² D

If a polynomial P(x) is divided by x - a, then the remainder is

• P(o) A
• P(-a) B
• P(a) C
• None of these D

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

• 4 A
• 3 B
• 50 C
• 7 D

• 15 A
• 9 B
• 7 C
• 8 D

• 0 A
• 1 B
• 2 C
• None of these 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

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

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

2x³+ 3x + 9 is a ______

• Polynomial of degree 3 A
• Quadratic equation B
• Cubic equation C
• Polynomial of degree 2 D

If a polynomial p(x) is divided by x-c, then the remainder is

• p(x) A
• x-c B
• c C
• P(c) D

For any integer k, wⁿ= ______ when n = 3k

• 1 A
• 2 B
• 0 C
• -4 D

4^1+x+ 4^1-x= 10 is called

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

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

• a > 0 A
• a < 0 B
• a≠ 0 C
• a≠ 0,b ≠ 0 D

• 
  A
• 
  B
• 
  C
• 
  D

• Linear equation A
• Quadratic equation B
• Cubic equation C
• None of these 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