    Question

# If the equation x4−4x3+ax2+bx+1=0 has four roots and all of them are positive real roots then the value of a and b are

A

a = 8, b = 6

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B

a = - 4, b = 8

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C

a = 6, b = - 4

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D

a = - 8, b = - 6

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Solution

## The correct option is B a = 6, b = - 4 We know, sum of the roots α+β+γ+δ=(−B)A=4 Since all the roots are positive. Sum of the roots taking 2 at a time should also be positive. Sum of the roots taking 2 at a time = a So, a should be positive a> 0 Sum of the roots taking 3 at a time = - b (it should also be positive) So, b must be less than zero b < 0 From the above given options only Option C satisfy the condition.  Suggest Corrections  0      Similar questions  Related Videos   MATHEMATICS
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