Question

If the equation $x^4-4x^3+a{x}^2+bx+1=0$ has four roots. All of them are positive real roots then value of a and b are given.

• A. a = 8, b = 6
• B. a = - 4, b = 8
• C. a = 6, b = - 4
• D. a = - 8, b = - 6

Answer 1

The correct option is C

a = 6, b = - 4

We know, sum of the roots

$\alpha +\beta +\gamma +\delta =\frac{(-B)}{A}=4$

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.