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

The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0

• 4 A
• 64 B
• 8 C
• All values of k D

Roots of the equation x²+ 5x - 1 = 0 are

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

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

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

• 0 A
• -1 B
• 1 C
• 2 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 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 roots of the equation ax²+ bx + c = 0 are real and equal if

• b²- 4ac < 0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these 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

• 
  A
• 
  B
• 
  C
• 
  D

w^-12= ______

• 0 A
• 1 B
• w C
• 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 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

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

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 quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is factor of x11+a11, where n is an odd integer

• x-a A
• x+a B
• 2x-a C
• 2x+a D

• 
  A
• 
  B
• 
  C
• 
  D

• 15 A
• 9 B
• 7 C
• 8 D

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

• 0 A
• -1-w² B
• 
  C
• 
  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

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

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

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

Which of the following is a factor of x³- 3x²+ 2x - 6

• x + 2 A
• x + 3 B
• x - 3 C
• x - 4 D

There are ______ basic techniques for solving a quadratic equation

• Two A
• Three B
• Four C
• None of these D

The vertex of the graph of the quadratic function f(x) = x2 -10, is

• (0 , -10) A
• (-10,0) B
• (10,0) C
• (0,10) D

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

• 
  A
• 
  B
• 
  C
• 
  D

If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is

• ay2 +2by+c=0 A
• ay2+2by+4c=0 B
• ay2+2by+c=0 C
• ay2+by+4c=0 D