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Quadratic Equations

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Question
SSCCGLENQA12044200
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The minimum value of (x - 2) (x - 9) is

  • negative 11 over 4

  • 49 over 4

  • 0

  • negative 49 over 4

Solution

D.

negative 49 over 4

(x - 2) (x - 9)
      = (x2 - 2x - 9x + 18) = (x2 - 11x + 18)
      As the co-efficient of x2 is greater than 0, 
∴ Minimum value of (x - 2) (x - 9) is given by,
      = (-D/4a)
      =  - (b2 - 4ac)/4a
      = - (121 - 4*1*18)/4*1
      = - (121 - 72)/4
     =   - 49/4
     

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Question
SSCCGLENQA12042140
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Which of the following equations has the sum of its roots?

  • x2 - 5x + 6 = 0

  • x2 - 5x - 6 = 0

  • x2 + 5x + 6 = 0

  • x2 + 5x - 6 = 0

Solution

A.

x2 - 5x + 6 = 0

x2 - 5x + 6 = 0
The sum of roots open parentheses straight alpha space plus space straight beta close parentheses is given by,
                         equals negative straight b over straight a space equals space fraction numerator negative left parenthesis negative 5 right parenthesis over denominator 1 end fraction space equals space 5

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