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

If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is

• 0 A
• 2 B
• 1 C
• 5 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

• b = c A
• a = c B
• a = c C
• b = 0 D

Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then

• α = β A
• αβ = 1 B
• α = β C
• α = 1 D

There are ______ basic techniques for solving a quadratic equation

• Two A
• Three B
• Four C
• None of these 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

If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then

• k=0 A
• k=1 B
• k=w C
• k=w2 D

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

• 1 A
• 2 B
• 0 C
• -4 D

w⁴= ______

• 0 A
• 1 B
• w C
• w² 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 maximum value of the quadratic function f(x) = -2x2+20x,is

• 4 A
• 3 B
• 50 C
• 7 D

The cube roots of 8 are

• 
  A
• 
  B
• 
  C
• 
  D

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

The graph of the quadratic equation is

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

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

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

If a polynomial P(x) is divided by x - a, then the remainder is

• P(o) A
• P(-a) B
• P(a) C
• None of these D

w¹¹= ______

• 0 A
• 1 B
• w C
• w² D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  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

w²⁹= ______

• 0 A
• 1 B
• w C
• w² D

(2 + w) (2 + w²) = ______

• 1 A
• 2 B
• 3 C
• 0 D

If a polynomial p(x) is divided by x-c, then the remainder is

• p(x) A
• x-c B
• c C
• P(c) D

The vertex of the graph of the quadratic function f(x) =-x2+6x+1,is

• (-3,10) A
• (-3,-10) B
• (3,10) C
• (3,-10) D

Which of the following is factor of x11+a11, where n is an odd integer

• x-a A
• x+a B
• 2x-a C
• 2x+a D

If f(x) = ax², and a>0, then the lowest point on the parabola is called.

• Vertex of parabola A
• Co-ordinates of parabola B
• Roots of the equation C
• Coefficient of the equation D

• Two real roots A
• Two positive roots B
• Two negative roots C
• One positive and one negative root D

The solution of equation x2 + 2 = 0 in the set of real number is

• Infinite set A
• Singleton set B
• Null set C
• None of these D