Asked by Trish Goal
Find all positive integer values of c such that the equation x^2-7x+c=0 only has roots that are real and rational.
Answers
Answered by
Steve
the two roots have product c and sum 7
Since the coefficient of x is 1, all the rational roots are integers.
(x-1)(x-6) = x^2-7x+6
(x-2)(x-5) = x^2-7x+10
...
I think you can see that there are only a few values for c.
Since the coefficient of x is 1, all the rational roots are integers.
(x-1)(x-6) = x^2-7x+6
(x-2)(x-5) = x^2-7x+10
...
I think you can see that there are only a few values for c.
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