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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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Answer:

Option D is correct.

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The complete question is contained in the attached image to this answer.

From the image attached and the additional information about the triangles, it is evident that that triangle VSW is similar to triangle QSR.

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Cross multiplying,

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Hope this Helps!!!

4 0
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