SOLUTION: find the value of k so that the equation 5x^2-8x+k=0 will have roots whose product is equal to 2/3?

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Question 495248: find the value of k so that the equation 5x^2-8x+k=0 will have roots whose product is equal to 2/3?

Answer by stanbon(57967) About Me  (Show Source):
You can put this solution on YOUR website!
find the value of k so that the equation 5x^2-8x+k=0 will have roots whose product is equal to 2/3?
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Roots are [8 +- sqrt(64 - 4*5*k)]/10
x = (4/5)+sqrt(64-20k)/10 and x = (4/5)-sqrt(64-20k)]/10
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Their product = (4/5)^2 - [(64-20k)/10]
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Solve for "k":
(4/5)^2 - [(64-20k)/10] = 2/3
(16/25) - 6.4 + 2k = 2/3
0.64-6.4+2k = 2/3
2k -5.76 = 2/3
k - 2.88 = 1/3
k = 3.2133
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Cheers,
Stan H.