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

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

• 3 A
• 5 B
• -3 C
• -5 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 A
• 4 B
• 8 C
• 16 D

The roots of (b-c)x2+(c-a) x+a-b=0 are equal if

• 2b = a+c A
• 2a = b+c B
• 2c = a+b C
• a + b + c =0 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 synthetic division method is only used to divide a polynomial by

• quadratic equation A
• binomial B
• linear equation C
• monomial 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

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

• 15 A
• 9 B
• 7 C
• 8 D

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

• 
  A
• 
  B
• 
  C
• 
  D

The roots of the equation 2^2x- 10.2^x+ 16 = 0 are

• 2, 8 A
• 1, 3 B
• 1, 8 C
• 2, 3 D

The condition for ax2 + bx c to be expressed as the product of linear polynomials is

• b4 - 4ac =0 A
• b4- 4ac ≥0 B
• b4- 4ac <0 C
• b4= 4ac D

The roots of (x - a)(x - b) = ab x2 are always

• Real A
• Depends upon a B
• Depends upon b C
• Depends upon a and b D

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

• 11 A
• 6 B
• -11 C
• 13 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

• 1 A
• -1 B
• 5 C
• 2 D

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² 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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• -1 A
• 0 B
• 2 C
• 1 D

In quadratic equation f(x) = ax²,if a >0, then the graph of parabola

• Opens up A
• Opens down B
• close up C
• symmetric w.r.t.x.axis 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

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

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 root of the quadratic equation are

• 3 A
• 2 B
• 1 C
• 4 D

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

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

Roots of the equation x²+ 2x + 3 = 0 are

• Real and equal A
• Real and distinct B
• Complex C
• None of these D

If a (p + q)²+ bpq +c = 0 and a (p + r)²+ 2 bpr + c = 0, then qr equals

• p²+ c/a A
• p²+ a/c B
• p²+ c/a C
• p²- c/a D