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

The product of cube roots of unity is

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

w²⁹= ______

• 0 A
• 1 B
• w C
• w² 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

• 0 A
• 1 B
• 2 C
• None of these 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

If the roots of ax2 + b =0 are real and distinct then

• ab > 0 A
• a = 0 B
• ab < 0 C
• a > 0,b > 0 D

The roots of the equation 4x - 3.2x+2 + 32 = 0 would include

• 1 and 3 A
• 1 and 4 B
• 1 and 2 C
• 2 and 3 D

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

• Negative A
• Positive B
• Zero C
• Nothing can be said D

The set of real roots of the equation log_{(5x + 4)}(2x +3)³- log_{(2x + 3)}(10x²+ 23x + 12) = 1 is

• {-1} A
• {-3/5} B
• Empty set C
• {-1/3} D

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

• 7 A
• -2 B
• 6 C
• 1 D

w⁷³= ______

• 0 A
• 1 B
• w C
• w² D

• 
  A
• 
  B
• 
  C
• 
  D

Another name of quadratic equation is

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

If S and P are the sum and the product of roots of a quadratic equation, then the quadratic equation is

• x²+ Sx - P = 0 A
• x²- Sx + P = 0 B
• x²- Sx - P = 0 C
• X²+ Sx + P = 0 D

• 
  A
• 
  B
• 
  C
• 
  D

If ax²+ bx + x = 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

The roots of (x - a)(x - b) = ab x2 are always

• Real A
• Depends upon a B
• Depends upon b C
• Depends upon a and b 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

• 15 A
• 9 B
• 7 C
• 8 D

A polynomial of arbitrary degree

• f(x) = o A
• f(x) = x B
• f(x) = a C
• f(x) = ax + b,a ≠ 0 D

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

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

A polynomial P(x)has a factor (x-a)if P(a) =

• a A
• x B
• 1 C
• 0 D

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

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

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

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

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

• 1 A
• 2 B
• 0 C
• -4 D

Two quadratic equation in which xy term is missing and the coefficients of x²and y²are equal, give a linear equation by ______

• Addition A
• Subtraction B
• Multiplication C
• Division D