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IceJOKER [234]
4 years ago
6

Write the left side of each equation as a product of linear factors, and state the solutions.

Mathematics
1 answer:
Amiraneli [1.4K]4 years ago
4 0

Answer:

a). x_{1}=1, x_{2}=1,x_{3}=1

b). x_{1}=2, x_{2}=2, x_{3}=2

c). x_{1} = \sqrt{-5}, x_{2} = \sqrt{-5}, x_{2} = \sqrt{-2},x_{4} = \sqrt{-2}

Step-by-step explanation:

a.

x^{3}-1=0\\x^{3}=1\\ x=(1 )^{\frac{1}{3} }

x=1

b.

x^{3}+8=0\\x^{3}=-8\\ x=(-8 )^{\frac{1}{3} }

x= 2i

c.

x^{4} +7x^{2} +10=0\\x^{4}=u^{2} \\x^{2}=u\\ u^{2}+7u+10=0\\

Using

\frac{-b+/-\sqrt{7^{2}-4*a*c } }{2*a}

u=\frac{-7+/-\sqrt{7^{2}-4*10}}{2}=-\frac{7}{2} +/- \frac{\sqrt{49-40} }{2} \\ u=-\frac{7}{2} +/- \frac{3}{2} \\u_{1}= -5\\u_{2}= -2

But u is no the factor is x so:

x=\sqrt{u}\\ x_{1} =\sqrt{-5} =5i\\ x_{2} =\sqrt{-2} =2i

Check:

(\sqrt{5i})^{4} +7*(\sqrt{5i})^{2}  +10=0\\25*i^{4} +7*5*i^{2}+10=0\\ 25*1+7*5*-1+10\\25-35+10=0\\0=0

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