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

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

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

• 0 A
• 1 B
• 2 C
• 3 D

• 
  A
• 
  B
• 
  C
• 
  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

The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

• Infinitely many roots A
• Exactly two roots B
• Exactly four roots C
• No roots D

The expression x2 - x + 1 has

• One proper linear factor A
• No proper linear factor B
• Two proper linear factors C
• None of these D

If one root of the equation x²- 3x + a = 0 is 2 then a = ______

• 0 A
• 1 B
• 2 C
• 3 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 roots of px2 - (p-q)x-q=0 are

• equal A
• Irrational B
• Rational C
• Imaginary D

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

• 
  A
• 
  B
• 
  C
• 
  D

The polynomial x - a is a factor of the polynomial f(x) if and only if

• f(a) is positive A
• f(a) is negative B
• f(a) = 0 C
• None of these 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

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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

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

• 7 A
• -2 B
• 6 C
• 1 D

• Two real roots A
• Two positive roots B
• Two negative roots C
• One positive and one negative root D

The standard form of the quadratic function f(x) = -x² +4x+2, is

• (x-2)²+6 A
• -(x-2)² + 6 B
• (x-3)²+5 C
• (x+4)²-7 D

If x - 2 is a factor of ax2- 12x + a = 2a, then a = ______

• -5 A
• 5 B
• 0 C
• 1 D

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

• Real A
• Imaginary B
• Positive C
• Negative D

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

• 0 A
• -1-w² B
• 
  C
• 
  D

If b²- 4ac = 0 then the roots of the equation are

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

• Polynomial of degree 0 A
• Polynomial of degree 1 B
• Polynomial of degree 2 C
• Polynomial of degree n D

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

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

Each complex cube root of unity is square of

• itself A
• 1 B
• -1 C
• the other D

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

• 0 A
• a³ B
• 2a³ C
• -2a³ D

x⁴- 3x³+ 3x + 1 = 0 is called ______

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

• 
  A
• 
  B
• 
  C
• 
  D

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D