Expert: Josh - 7/27/2007

Question
z2-14z + 49

z=2 to the second power

Answer
Hi Pat,

I'm not sure what the question is asking.

Are you saying that z=2^2 and we have to evaluate the expression at z=4?

If this is the case, then
z^2-14z+49 = 4^2-14*4+49 = 16-56+49. The answer is 9

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If we have to find the roots (solutions) of the quadratic equation, and you are just telling me that z^2 represents "z square", we proceed as follows.

Factorize the quadratic expression and set this to zero in order to find the solutions.

Observe that z^2-14z+49 = (z-7)(z-7). We have a perfect square factorization. Setting this zero, (z-7)(z-7)=0 only when z=7. When the two solutions are identical, we say there's a repeated root.

Hope this answers your question.