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What is the sum of the the roots of the equation 4x^3 + 5x^2 - 8x = 0 ? Express your answer as a decimal to the nearest hundredth.

 Jul 20, 2023
 #1
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We can factor the equation as 4x(x2+45​x−2)=0. The first factor, 4x, never equals 0, so the only way the equation is true is if x2+45​x−2=0. By the quadratic formula, the roots of this equation are

[x = \frac{-5 \pm \sqrt{25 + 16}}{2} = -\frac{5 \pm 7}{2}.]The sum of the roots is then 2−5−5+7+7​ = 1.0​.

 Jul 20, 2023
 #2
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x = 0


x = 1/8 (-5 - 3 sqrt(17))


x = 1/8 (3 sqrt(17) - 5)

 

Sum = 0 + 1/8 (-5 - 3 sqrt(17)) + 1/8 (3 sqrt(17) - 5)= - 5/4 = - 1.25

 Jul 20, 2023

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