if both the roots of the equation x2+bx+b=0 are the roots of the equation x3+3x2+3x+2=0. find b
Answers
Answered by
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Step-by-step explanation:
It is given that the roots are −1,2+
3
,2−
3
Hence the cubic equation is
(x+1)(x−(2−
3
))(x−(2+
3
))=0
(x+1)(x
2
−(2−
3
+2+
3
)x+(2−
3
)(2+
3
)=0
(x+1)(x
2
−4x+(4−3))=0
(x+1)(x
2
−4x+1)=0
x
3
−4x
2
+x+x
2
−4x+1=0
x
3
−3x
2
−3x+1=0
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