Question

If the equation $x^4-3x^3+m{x}^2-7x+3=0$ has four positive real roots. Then,

• A. the value of $m$ should always be greater than zero.
• B. None of these
• C. the value of $m$ should be zero
• D. the value of $m$ should always be less than zero.

Answer 1

The correct option is A the value of $m$ should always be greater than zero.

The given equation is $x^4-3x^3+m{x}^2-7x+3=0$

According to the relation between roots and coefficients of higher degree equations,
Sum of the roots taken two at a time

$\sum \alpha \beta =m$

Since all the roots are positive real numbers

$m$ should also be positive

$\Rightarrow m>0.$