Question 1136677: The value of q for which the difference between the roots of the equation x^2-qx+8=0 is 2 are
+-2
+-4
+-6
+-8
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
I easily can guess: the roots 2 and 4 gives the product of 8 (the constant term) and the difference of 2.
Their sum is 6, which should be " q", according to Vieta's theorem.
So, the answer is q = 6, based on my guessing.
Let's look what the Algebra solution will give us.
Let x and (x-2) are the roots.
Then their product is 8:
x*(x-2) = 8
x^2 - 2x - 8 = 0
(x-4)*(x+2) = 0.
So, there are 2 roots: x= 4 and x= -2.
The value x= 4 gives that two roots 4 and 2 which I guessed above, with the value of q= 6.
The value x= -2 gives two roots -2 and -4, with the value of q = -6.
So, the problem has two answers: q= 6 and q= -6. (Third line of the answers' choice)
Thus Algebra solution helped me to find 2 answers to the problem question: more than I could guess (!)
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
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.
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.
And those roots make q either 6 or -6.
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.
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