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

a. x^3 − 1 = 0
b. x^3 + 8 = 0
c. x^4 + 7x^2 + 10 = 0

User Raymundo
by
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1 Answer

5 votes

Answer:

a).
x_(1)=1,
x_(2)=1,
x_(3)=1

b).
x_(1)=2,
x_(2)=2,
x_(3)=2

c).
x_(1) = √(-5),
x_(2) = √(-5),
x_(2) = √(-2),
x_(4) = √(-2)

Explanation:

a.


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


x=1

b.


x^(3)+8=0\\x^(3)=-8\\ x=(-8 )^{(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}=-(7)/(2) +/- (√(49-40) )/(2) \\ u=-(7)/(2) +/- (3)/(2) \\u_(1)= -5\\u_(2)= -2

But u is no the factor is x so:


x=√(u)\\ x_(1) =√(-5) =5i\\ x_(2) =√(-2) =2i

Check:


(√(5i))^(4) +7*(√(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

User JustLogin
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