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

• 
  A
• 
  B
• 
  C
• 
  D

Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if

• c = 0 A
• c = 0,b≠ 0 B
• b = 0,c = 0 C
• b = 0,c≠ 0 D

If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is

• 1 A
• 3 B
• 2 C
• 4 D

If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is

• 0 A
• ±1 B
• ±5 C
• ±7 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

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

2x³+ 3x + 9 is a ______

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

The roots of ax2+bx+c=0 are

• Rational ⇔ b2 -4 ac ≥ 0 A
• Irrational ⇔ b2-4 ac > 0 B
• Real ⇔ b2-4 ac ≠ 0 C
• Rational⇔ b2-4 ac = 0 D

w⁴= ______

• 0 A
• 1 B
• w C
• w² D

• 1 A
• 2 B
• 0 C
• 4 D

The value of k (k > 0) for which the equation x²+ kx + 64 = 0 and x²- 8x + k = 0 both will have real roots is

• 8 A
• -16 B
• -64 C
• 16 D

• Rational A
• Irrational B
• Non-real C
• Zero 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

The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in

• 
  A
• 
  B
• 
  C
• 
  D

The roots of the equation ax²+ bx + c = 0 are complex/imaginary if

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

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

• Rational A
• Irrational B
• Complex C
• None of these 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 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 the roots of 3x2+kx + 12 = 0 are equal then k = ______

• 
  A
• 
  B
• 
  C
• 
  D

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

• -5 A
• 5 B
• 0 C
• 1 D

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

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

Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when

• q = 0, r = 0,p ≠ 0 A
• p = 0,qr≠ 0 B
• r = 0,pq≠ 0 C
• q = 0, pq≠ 0 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

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

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

Another name of quadratic equation is

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

The minimum value of the quadratic function f(x) = 5 x 2-11,is

• -11 A
• 6 B
• -7 C
• 7 D

If the roots of ax²+ bx + c =0 are equal in magnitude but opposite in sign, then

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