The number of integral values of m for which the quadratic expression.
$(1 + 2 m) x^{2} - 2 (1 + 3 m) x + 4 (1 + m), x \in R$ , is always positive, is:

8

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

7

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

6

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!

Open in App

Solution

The correct option is B $7$
$a x^{2} + b x + c$ is always positive if $a > 0$ and $D = b^{2} - 4 a c < 0$
Expression is always positive it
$2 m + 1 > 0 \Rightarrow m > - \frac{1}{2}$
&
$D < 0 \Rightarrow m^{2} - 6 m - 3 < 0$
$3 - \sqrt{12} < m < 3 + \sqrt{12}$
$∴$ integral value of m $0, 1, 2, 3, 4, 5, 6$

Suggest Corrections

Similar questions

m

(1 + 2 m) x^{2} - 2 (1 + 3 m) x + 4 (1 + m), x \in R,

m

(1 + 2 m) x^{2} - 2 (1 + 3 m) x + 4 (1 + m), x \in R,

m

(1 + 2 m) x^{2} - 2 (1 + 3 m) x + 4 (1 + m), x \in R,

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

m \in R - {- 1})

^{'} m^{'}

m

y = (m^{2} - 9) x^{2} + (m - 3) x - 7

- 1

Join BYJU'S Learning Program