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Question

If the equation x44x3+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 C

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.


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