SOLUTION: One exact x-intercept of y= x^2+kx+1 is 3+2root2.What is the value of k ?

Question 114150: One exact x-intercept of y= x^2+kx+1 is 3+2root2.What is the value of k ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One exact x-intercept of y= x^2+kx+1 is 3+2root2.What is the value of k ?
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x^2+kx+1 = y
At the x-intercept, y = 0.
f(3+sqrt2) = (3+sqrt2)^2 + k(3+sqrt2) + 1 = 0
9+6sqrt2+2 + k(3+sqrt2) +1 =0
k(3+sqrt2) = -(6sqrt2 +12)
k = -6(sqrt2+2)/(3+sqrt2)
Multiply numerator and denominator by 3-sqrt2 to get:
k = -6(2+sqrt2)(3-sqrt2)/(9-2)
k = -(6/7)[6+sqrt2-2)
k = -(6/7)[4+sqrt2]
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Cheers,
Stan H.
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