SOLUTION: If (2x-1) is a factor of f(x)=2x^3-5x^2-kx+3 find the value of k. Find the other two factors of f(x) and solve the equation f(x)=0

Question 366928: If (2x-1) is a factor of f(x)=2x^3-5x^2-kx+3 find the value of k.
Find the other two factors of f(x) and solve the equation f(x)=0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If (2x-1) is a factor of f(x)=2x^3-5x^2-kx+3 find the value of k.
Find the other two factors of f(x) and solve the equation f(x)=0
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Using synthetic division:
1/2)....2....-5....k....3
.........2.....-4...k-2..|3+[(k-2)/2]
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solve 3 + (k-1)/2 = 0 for "k":
6 + (k-1) = 0
k-1 = -6
k = -5
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Substitute for "k" and solve the quotient:
2x^2 -4x - 7 = 0
Use the quadratic formula:
x = [4 +- sqrt(16-4*2*-7)]/4
x = [4 +- sqrt(72)]/4
x = [4 +- 6sqrt(2)]/4
x = 1 + (3/2)sqrt(2) or x = 1-(3/2)sqrt(2)
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You now have three solutions for f(x) = 0
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Cheers,
Stan H.
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