Solve x3 - 8x2 + 9x + 18 = 0, given that two of its roots are in the ratio 1:2. =
Answers
Answer:
p(x)=x
5
−x
4
+8x
2
−9x−15=0
If
3
is one root then −
3
is also a root
⇒(x−
3
)(x+
3
) is a factor of p(x)
⇒x
2
−3 is a factor of p(x)
Dividing p(x) by ⇒x
2
−3
p(x)=(x
3
−x
2
+3x+5)(x
2
−3)
Let q(x)=x
3
−x
2
+3x+5
Now (−1−2i) is a factor of q(x) then (−1+2i) is also a factor
⇒{x−(−1−2i)}{x−(−1+2i)} is a factor of q(x)
⇒(x+1)
2
−(2i)
2
is a factor of q(x)
⇒x
2
+2x+5 is a factor of q(x)
Dividing q(x) by x
2
+2x+5
⇒q(x)=(x+1)(x
2
+2x+5)
⇒(x+1)(x
2
+2x+5)=0
⇒x+=0
⇒x=−1
So the remaining root is −1
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Step-by-step explanation:
hanges made to your input should not affect the solution:
(1): "y2" was replaced by "y^2". 1 more similar replacement(s).
Unauthorized use of the imaginary unit "i" or syntax error in complex arithmetic expression
....... V
multiply^3-8multjply^2-9multiply+18=0
The symbol "i" is only allowed in complex arithmetic, for example:
(3/5+7i)+(0.3-7.002i)
(5+77i)-(19/4-8i)
(240-22i)*(247/7+2.222i)
(33/5+99i)/(33/5-88i)
Unauthorized use of the imaginary unit "i" or syntax error in complex arithmetic expression