Math, asked by itsleela18, 10 months ago

Solve the equation x4 − 4x2 + 8x + 35 = 0, if one of its roots is
2 + 3 i

Answers

Answered by vickey90
2

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Since 2+i

3

is a root and the coefficients are real, the second root has to be 2−i

3

Thus, (x−2−i

3

)(x−2+i

3

)=x

2

−2x+ix

3

−2x+4−i2

3

−ix

3

+i2

3

+3

=x

2

−4x+7 is a root of the given equation.

Dividing the original equation by x

2

−4x+7, we have

(x

4

−4x

2

+8x+35)/(x

2

−4x+7)=x

2

+4x+5

Thus, we obtain the other root as x

2

+4x+5

Again factorizing this root, we get x=

2

−4±

16−20

=

2

−4±2i

=−2±i

The four roots are therefore 2+i

3

,2−i

3

,−2+i,−2−i

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