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

Which of the following is factor of p(x) =2x3 +3x2+3x+2 ?

• x+1 A
• 2x+1 B
• 3x+1 C
• 2x-1 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

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

• 
  A
• 
  B
• 
  C
• 
  D

If the roots of ax²+ bx + c = 0 (a > 0) be greater than unity, then

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

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

• 1 A
• 2 B
• 0 C
• -4 D

w^-12= ______

• 0 A
• 1 B
• w C
• w² D

Roots of the equation x²- x = 2 are

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

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

• -5 A
• 5 B
• 0 C
• 1 D

The minimum value of the quadratic function f(x) = x2 +6x -2, is

• 11 A
• 6 B
• -11 C
• 13 D

The discriminant of the quadratic equation ax²+ bx + c = 0 is

• b²+ 4ac A
• b²- 4ac B
• 4ac - b² C
• a²- 4ac D

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

• 2 A
• 1 B
• 0 C
• -1 D

(x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if

• a+b=c+d A
• a+c=b+d B
• a+d=b+c C
• All are correct D

w⁷³= ______

• 0 A
• 1 B
• w C
• w² D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

If 3x⁴+ 4x³+ x - 5 is divided by x + 1, then the reminder is

• 0 A
• 7 B
• -7 C
• 5 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

• -1 A
• 0 B
• 2 C
• 1 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

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

• 0 A
• -1-w² B
• 
  C
• 
  D

The standard form of the quadratic function f(x) = -x² +4x+2, is

• (x-2)²+6 A
• -(x-2)² + 6 B
• (x-3)²+5 C
• (x+4)²-7 D

If the roots of ax²- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is

• 
  A
• 
  B
• 
  C
• 
  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

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 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

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

• 0 A
• a³ B
• 2a³ C
• -2a³ D

• 
  A
• 
  B
• 
  C
• 
  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