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

the value of m should always be less than zero.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

the value of

m

should be zero

No worries! We‘ve got your back. Try BYJU‘S free classes today!

the value of m should always be greater than zero.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C the value of m should always be greater than zero.
The given equation is $x^{4} - 3 x^{3} + m x^{2} - 7 x + 3 = 0$

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

$\sum α β = m$

Since all the roots are positive real numbers

m should also be positive

So, m > 0.

Suggest Corrections

Similar questions

x^{4} + p x^{3} + q x^{2} + r x + 5 = 0

p r

The equation (m being real), $m x^{2} + 2 x + m = 0$ has two distinct roots if ___.

x^{4} + 3 x^{3} - 2 x^{2} - 3 = 0

λ x^{2} - 2 x + 3 = 0

λ

Join BYJU'S Learning Program