Question 1136677
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According to Vieta's Theorem, for the given equation x^2-qx+8=0, the product of the roots is 8 and the sum of the roots is q.<br>
Then, given that the difference between the two roots is 2, a very little bit of mental arithmetic (product of two numbers = 8; difference = 2) finds two solutions -- roots of 2 and 4, or roots of -2 and -4.<br>
And those roots make q either 6 or -6.<br>
ANSWER: The third choice, -6, is ONE OF the values for q for which the difference between the two roots of the equation is 2.