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