ECAT Mathematics Chapter 6 Quadratic Equations

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

• 0 A
• 7 B
• -7 C
• 5 D

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

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

Ifα,βare the roots of ax²+ bx + c = 0 andα+ h,β+ h are the roots of px²+ qx + r=0, then h =

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  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

The roots of the equation 4x - 3.2x+2 + 32 = 0 would include

• 1 and 3 A
• 1 and 4 B
• 1 and 2 C
• 2 and 3 D

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

• 1 A
• 2 B
• 1 and -7 C
• -7 D

• 0 A
• 1 B
• 2 C
• None of these D

Sum of all the four forth roots of unity is

• 1 A
• -1 B
• i C
• 0 D

• 
  A
• 
  B
• 
  C
• 
  D

The quadratic formula is

• 
  A
• 
  B
• 
  C
• 
  D

If sinαand cosαare the roots of the equation px²+ qx + r =0, then

• p²- q²+ 2pr = 0 A
• (p + r)²= q²- r² B
• p²+ q²- 2pr = 0 C
• (p - r)²= q²+ r² D

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

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

• 1 A
• -1 B
• 5 C
• 2 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

The quadratic equation 8 sec²θ- 6 secθ+1 = 0 has

• Infinitely many roots A
• Exactly two roots B
• Exactly four roots C
• No roots D

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

• 3 A
• 5 B
• -3 C
• -5 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

• 
  A
• 
  B
• 
  C
• 
  D

The synthetic division method is only used to divide a polynomial by

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

The roots of px2 - (p-q)x-q=0 are

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

• 
  A
• 
  B
• 
  C
• 
  D

The equation (cos p - 1)x²+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval

• (0, 2π) A
• (-π, -0) B
• (0,π) C
• None of these 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

• 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
• 0 B
• 2 C
• 1 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

• 1 A
• 2 B
• 0 C
• 4 D

(1+w)(1+w2)(1+w4)(1+w8)....50 factors

• 0 A
• -1 B
• 1 C
• 2 D