SOLUTION: If r and s are the roots of x^2 -8x +6 =0, find r^2 + 3rs +s^2. Thank you.

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Question 1011284: If r and s are the roots of x^2 -8x +6 =0, find r^2 + 3rs +s^2. Thank you.
Found 3 solutions by solver91311, ikleyn, MathTherapy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

Use the quadratic formula to determine the roots of , leaving them in simplest exact form. The rest is just arithmetic.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
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If r and s are the roots of x^2 -8x +6 =0, find r^2 + 3rs +s^2.
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You do not need to solve the equation and manipulate with the roots to answer the question. If r and s are the roots of the equation = , then r + s = 8, rs = 6. *) see an explanation below, after the problem' solution. Then = = 64. Add rs = 6 to both sides, and you will get = 64 + 6 = 70. Answer. = 70. ---------------------------------------------- *) If r and s are the roots of the equation = , then the factorization takes place = (x-r)*(x-s). If you open parentheses, you will get r + s = -p and rs = q. The problem in the claim is aimed to teach the student these identities and to teach him/her to apply them.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!
If r and s are the roots of x^2 -8x +6 =0, find r^2 + 3rs +s^2. Thank you.

Sum of roots: , or , or 8
Product of roots: , or , or 6
Therefore, r + s = 8, and rs = 6
, but , so , or 64 + 6, or