college algebra

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Solve the following equation in the complex number system. Please show all of your work.
2x^5-3x^4-32x+48=0

• college algebra -

solving quintics is hard, so look for easy roots with synthetic division

2x^5-3x^4-32x+48
(x+2)(x-2)(2x-3)(x^2+4)
= (x+2)(x-2)(2x-3)(x-2i)(x+2i)

• college algebra -

The manager of a coffee shop has one type of coffee that sells for \$5 per pound and another type that sells for
\$11 per pound. The manager wishes to mix 60 pounds of the \$11 coffee to get a mixture that will sell for \$9 per
pound. How many pounds of the \$5 coffee should be used?

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