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If `alpha_(1),alpha_(2),alpha_(3), alpha_(4)` are the roos of `x^(4)+2x^(3)+bx^(2)+cx+d=0` such that `alpha_(1)-alpha_(3)=alpha_(4)-alpha_(2)`, then `b-c` is equal to__________ |
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Answer» Correct Answer - 1 `(x^(4)+2x^(3)+bx^(2)+cx+d)=(x-alpha_(1))(x-alpha_(2))(x-alpha_(3))(x-alpha_(4))=(x^(2)+px+q)(x^(2)+px+r)` `=x^(4)+2px^(3)+(q+r+p^(2))x^(2)+(pr+pq)x+qr` `(2p)^(3)-4(2p)(q+r+p^(2))+8(pq+pr)=0` `2^(3)-4xx2xxb+8c=0` `impliesb-c=1` |
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