The number of integral values of $m$ for which the equation $(1 + m^{2}) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0$ has no real root is :

2

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

3

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

infinitely many

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

1

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

Open in App

Solution

The correct option is C infinitely many
Given quadratic equation has no real root.
$\Rightarrow D < 0$
$\Rightarrow 4 (1 + 3 m)^{2} - 4 (1 + m^{2}) (1 + 8 m) < 0$
$\Rightarrow 1 + 9 m^{2} + 6 m - 1 - 8 m - m^{2} - 8 m^{3} < 0$
$\Rightarrow 8 m^{3} - 8 m^{2} + 2 m > 0$
$\Rightarrow 2 m (2 m - 1)^{2} > 0$
$\Rightarrow m > 0 {m \neq \frac{1}{2}}$

Suggest Corrections

Similar questions

(1 + m^{2}) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0

(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0

m \in R - {- 1})

^{'} m^{'}

(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0

m

(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0

(m \in R)

(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m) = 0

m \in R - {- 1})

m

2 : 3

Join BYJU'S Learning Program