SOLUTION: find all the zeroes of x²+(3-√2)x-3√2 if one of its zero is √2?

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Question 1126944: find all the zeroes of x²+(3-√2)x-3√2 if one of its zero is √2?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


-3 by inspection


John

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

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

The Vieta's formula (theorem) says that the product of two roots of this quadratic equation is the constant term:


    alpha.beta = -3%2Asqrt%282%29.


Since one of the roots is  sqrt%282%29,  the other root is  %28-3%2Asqrt%282%29%29%2Fsqrt%282%29 = -3.


Exactly as the other tutor states - but with an appropriate explanation.