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

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

The roots of px2 - (p-q)x-q=0 are

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

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

• 0 A
• a³ B
• 2a³ C
• -2a³ D

A quadratic equation has two

• roots A
• degree B
• variables C
• constants D

The maximum value of the quadratic function f(x) = -2x2+20x,is

• 4 A
• 3 B
• 50 C
• 7 D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

In quadratic equation y=ax³ +bx+c, if b and c are both zero then the graph is

• Symmetric w.r.t.y-axis A
• Symmetric w.r.t.x-axis B
• Straight Line C
• Circle D

Another name of quadratic equation is

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

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

The solution set of x²- 5x + 6 = 0 is

• {1, 3} A
• {2, 3} B
• {1, 2} 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

x⁴- 3x³+ 3x + 1 = 0 is called ______

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

The maximum value of the quadratic function f(x) = 2x2-4x+7,is

• 3 A
• 5 B
• -3 C
• -5 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 a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is

• 8 A
• 12 B
• 10 C
• 14 D

The root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

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

The graph of a quadratic function is

• Circle A
• Ellipse B
• Parabola C
• Hexagon 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

• 1 A
• 2 B
• 0 C
• 4 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

The condition for polynomial equation ax²+ bx + c = 0 to be quadratic is

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 2 C
• 3 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

• (a - c)²= b²- c² A
• (a - c)²= b²+ c² B
• (a + c)²= b²- c² C
• (a + c)²= b²+ c² D

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

• Polynomial of degree 0 A
• Polynomial of degree 2 B
• Quadratic equation C
• None of these D

w¹¹= ______

• 0 A
• 1 B
• w C
• w² D

• 4 A
• 6 B
• 8 C
• 10 D