Math, asked by tanvvi4565, 1 year ago

What should be added to 4p^2 - 12p + 6 to make it a perfect square

Answers

Answered by knjroopa
5

Step-by-step explanation:

Given What should be added to 4p^2 - 12p + 6 to make it a perfect square .

  • Any quadratic equation is of the form ax^2 + bx + c = 0
  • Here d = b^2 – 4ac
  • It is 0 for a perfect square.
  • So we get 0 = 144 – 4(4)(c)
  •               16 c = 144
  •   So c = 144/16
  • So c = 9
  • So given equation is 4p^2 – 12p + 6. We need to make this equation a perfect square by adding a number. So we need to add 3 to the given equation.
  • Upon adding 3 to the equation we get
  • 4p^2 – 12p + 6 + 3
  • So now the equation will be
  • 4p^2 – 12p + 9
  • This equation is a perfect square because we get (2p – 3)^2 which is of the form  
  • (a – b)^2 = a^2 – 2ab + b^2
  • So 3 should be added.
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