Which of the following is not a perfect square. A. x^2+4x+16 B. x^2+6x+9  C. 4x^2+4x+1 D. 1-2x+x^2 E. 9x^2-6x+1

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Let us consider the general form of a quadratic equation.

`ax^2+bx+c = 0`

When we have a perfect square that means we have the following combination.

`b^2-4ac = 0`

 

`A. x^2+4x+16`

`b^2-4ac = 16-4xx1xx16 = -48`

 

`B. x^2+6x+9`

`b^2-4ac = 6^2-4xx1xx9 = 0`

 

`C. 4x^2+4x+1`

`b^2-4ac = 16-4xx4xx1 = 0 `

 

`D. 1-2x+x^2`

`b^2-4ac = (-2)^2-4xx1xx1 = 0 `

 

`E. 9x^2-6x+1`

`b^2-4ac = (-6)^2-4xx9xx1 = 0`

 

So the answer is A.

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