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

The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is

• 2 A
• 1 B
• -1 C
• -2 D

Another name of quadratic equation is

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

w¹⁵= ______

• 0 A
• 1 B
• w C
• w² D

If one root of the equation x²- 3x + a = 0 is 2 then a = ______

• 0 A
• 1 B
• 2 C
• 3 D

• 0 A
• -1-w² B
• 
  C
• 
  D

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

• 4 A
• 3 B
• 50 C
• 7 D

The expression x2 - x + 1 has

• One proper linear factor A
• No proper linear factor B
• Two proper linear factors C
• None of these D

The roots of the equations will be equal if b²- 4ac is

• Positive A
• Negative B
• 1 C
• Zero D

w²⁸+ w³⁸= ______

• 0 A
• 1 B
• w C
• -1 D

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

• 0 A
• 7 B
• -7 C
• 5 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 roots of px2 - (p-q)x-q=0 are

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

The roots of the equation ax²+ bx + x = 0 are real and distinct if

• b²- 4ac <0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these 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

The sum of the roots of the equation x2 -6x +2 = 0 is

• -6 A
• 2 B
• -2 C
• 6 D

If x - 1 is a factor of x4 - 5x2 + 4 then other factor is

• (x + 2)2(x - 1) A
• (x + 2)(x - 1)2 B
• (x+2)(x2- x- 2) C
• (x + 2)2(x - 1)2 D

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 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

If x³- x²+ 5x+ 4 is divided by x - 2, then the reminder is

• 0 A
• 2 B
• 18 C
• 14 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

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

• 1 A
• 2 B
• 0 C
• -4 D

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

• 2 A
• 1 B
• 0 C
• -1 D

The roots of the equation ax²+ bx + c = 0 are complex/imaginary if

• b²- 4ac < 0 A
• b²- 4ac = 0 B
• b²- 4ac > 0 C
• None of these D

(x-1) is a factor of

• 2x³-3x²+9 A
• 2x³-5x-8 B
• 48x^2-46x-9 C
• x⁹-1 D

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

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

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

• 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

• 1 A
• 2 B
• 0 C
• 4 D