If α and β are roots of ax + bx + c = 0, the

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 Multiple Choice QuestionsMultiple Choice Questions

51.

If z1 , z2, z3 are imaginary numbers such that z1 = z2 = z3 = 1z1 + 1z2 + 1z3 = 1, then z1 + z2 + z3 is

  • equal to 1

  • less than

  • greater than 1

  • equal to 3


52.

If p.q are the · roots of the equation x2 + px + q =0, then

  • p = 1, q = - 2

  • p = 0, q = 1

  • p = - 2, q = 0

  • p = - 2, q = 1


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53.

If α and β are roots of ax + bx + c = 0, then the equation whose roots are α2 and β2 is

  • a2x2 - (b2 - 2ac)x + c2 = 0

  • a2x2 + (b2 - ac)x + c2 = 0

  • a2x2 + (b2 + ac)x + c2 = 0

  • a2x2 + (b2 + 2ac)x + c2 = 0


A.

a2x2 - (b2 - 2ac)x + c2 = 0

Now, if the roots are α2 and β2, then

α2 + β2 = α + β2 - 2αβ             = - ba2 - 2ca             = b2a2 - 2caAnd α2β2 = αβ2 = ca2 = c2a2

The equation whose roots are α2 and β2, is

x2 - b2a2 - 2cax + c2a2 = 0 a2x2 - b2 - 2acx + c2 = 0


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54.

If the equation x2 + y2 - 10x + 21 = 0 has real roots x = α and y = β, then

  • 3  x  7

  • 3  y  7

  • - 2  x  2

  • - 2  x  2


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55.

If α and β are the roots of x2 - px +1 = 0 and γ is aroot of x2 + px +1 = 0, then α + γβ + γ is

  • 0

  • 1

  • - 1

  • ρ


56.

The quadratic expression 2x +12 - px + q  0 for any real x, if

  • p2 - 16p - 8q < 0

  • p2 - 8p + 16q < 0

  • p2 - 8p - 16q < 0

  • p2 - 16p + 8q < 0


57.

Let f: R  R be defmed as f(x) = x2 - x + 4x2 +  x + 4 Then, range of the function f(x) is

  • 35, 53

  • 35, 53

  • - , 35  53, 

  • - 53, - 35


58.

The least value of 2x2 + y2 + 2xy + 2x -3y + 8 for real numbers x and y, is

  • 2

  • 8

  • 3

  • - 1/2


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59.

Find the maximum value of z when z - 3z = 2, where z being a complex number.

  • 1 + 3

  • 3

  • 1 + 2

  • 1


60.

Given that, x is a real number satisfying 5x2 - 26x + 53x2 - 10x + 3 < 0, then

  • x < 15

  • 15 < x < 3

  • x > 5

  • 15 < x < 13 or 3 < x < 5


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