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

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

• 4 A
• 6 B
• 8 C
• 10 D

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

• 1 A
• 2 B
• 0 C
• -4 D

The product of cube roots of unity is

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

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

• p²- q²+ 2pr = 0 A
• (p + r)²= q²- r² B
• p²+ q²- 2pr = 0 C
• (p - r)²= q²+ r² 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

A quadratic equation in x is an equation that can be witten in the form

• ax² + b = 0 A
• ax³ +b²+c=0 B
• ax² +bx+c=0 C
• ax³ +bx³+cx=0 D

w^-1= ______

• 0 A
• 1 B
• w C
• w² D

• 15 A
• 9 B
• 7 C
• 8 D

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

• -11 A
• 6 B
• -7 C
• 7 D

w⁷³= ______

• 0 A
• 1 B
• w C
• w² D

Root of the equation 3^x-1+ 3^1-x= is

• 2 A
• 1 B
• 0 C
• -1 D

2x³+ 3x + 9 is a ______

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

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

The graph of the quadratic equation is

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

• 
  A
• 
  B
• 
  C
• 
  D

The solution of the quadratic equation x2 -7x + 10=0, is

• 2 A
• 5 B
• 2,5 C
• 7 D

w⁴= ______

• 0 A
• 1 B
• w C
• w² D

A quadratic equation has two

• roots A
• degree B
• variables C
• constants 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

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

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

Roots of the equation x²- x = 2 are

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

For the equation |x²| + |x| -6 =0, the roots are

• One and only one real number A
• Real with sum one B
• Real with sum zero C
• Real with product zero D

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

• (x + 2)2(x - 1) A
• (x + 2)(x - 1)2 B
• (x+2)(x2- x- 2) C
• (x + 2)2(x - 1)2 D

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

• 
  A
• 
  B
• 
  C
• 
  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

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 x²- 7x + a has remainder 1 when divided by x + 1, then a = ______

• -7 A
• 7 B
• 0 C
• None of these 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