Integer roots are assessed.
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Note the polynomial form P(x) = x2 - a. And, note that the two linear factors ( x + a ) ( x - a ), when multiplied together, yield
( x + a ) ( x - a ) = x2 - a.
Consequently, we note that an equation of the form
x2 - a= 0
can be factored as
( x + a ) ( x - a ) = 0,
giving the two zeros of our equation
x = a, -a.
DQ 5: For an arbitrary integer a and an equation of the form x2 - a = 0, how would you use the response of DQ 2 to determine if our two zeros are, indeed, integers? Can you exhibit an example?
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This solution is comprised of an explanation of how to assess integer roots.
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Suppose that for the equation x^2 - a = 0, we have two integer roots n and m (n and m could be positive or negative), then x^2 - a = (x + n)(x + m) = 0. You can see easily that n or m does not equal ...
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