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Question

For equation x42x32x2+18x63=0 if two of its roots are equal in magnitude but opposite in sign. Then other two roots are


A

Imaginary

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B

Real and negative

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C

None of these

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D

Real and positive

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Solution

The correct option is A

Imaginary


Given: x42x32x2+18x63=0...(1)

Let roots be α,β,γ,δ.

It is given that α+β=0

Using the relation between roots and coefficeints of a polynimial equation
α+β+γ+δ=2γ+δ=2

Let αβ=p and γδ=q

Bi-quadratic equation ( x2 + p) ( x22x+q) ______ (2)

Compare the coefficient of equation 1 and 2

p + q = - 2, -2p = 18, pq = - 63

p = -9, q = 7

pq = - 63 (satisfies)

Biquadratic equation is

( x2 - 9) ( x22x+7)=0

Roots are ± 3 and 1± i 6 Other two roots are complex number.


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