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

If ax + bx + c =0 is satisfied by every value of x,then

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

• 
  A
• 
  B
• 
  C
• 
  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

If one root of the equation ix²- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is

• -i A
• 2 + i B
• i C
• 2 - i D

• 
  A
• 
  B
• 
  C
• 
  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

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 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

The product of the four fourth roots of unity is

• 0 A
• 1 B
• -1 C
• None of these D

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

the largest degree of the terms in the polynomials is called

• terms of the polynomial A
• degree of a polynomial B
• co-efficient C
• monomial D

• 
  A
• 
  B
• 
  C
• 
  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

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

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

• 0 A
• 1 B
• 2 C
• None of these D

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

If the roots of x²+ ax + b = 0 are non-real, then for all real x, x²+ ax + b is

• Negative A
• Positive B
• Zero C
• Nothing can be said D

• 0 A
• -1-w² B
• 
  C
• 
  D

The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in

• 
  A
• 
  B
• 
  C
• 
  D

The two parts into which 57 should be divided so that their product is 782 are

• 43,14 A
• 34,23 B
• 33,24 C
• 44,13 D

The roots of the equation x2 +6x-7=0,are

• 1 A
• 2 B
• 1 and -7 C
• -7 D

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

w⁷³= ______

• 0 A
• 1 B
• w C
• w² D

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

• 2 A
• 5 B
• 2,5 C
• 7 D

• n if n is even A
• 0 for any natural number n B
• 1 if in odd C
• None of these D

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

Both the roots of the equation (x -b) (x - c ) + (x -c) (x-a) +(x-a) (x-b) = 0 are always

• Positive A
• Negative B
• Real C
• None of these D

The product of cube roots of unity is

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

A quadratic equation has two

• roots A
• degree B
• variables C
• constants 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