Question

If
mx^2 -9mx + 5m +1 >0 for all x
and x belongs to R , then m lies in the interval

Answer 1

m should not be negative. Can you please re-confirm the answer ?

Answer 2

sorry
(0 , 4/ 61 )

Answer 3

hmm.
so your polynomial p(x) > 0 for all x in R.
Which means 2 things :
1) Graph of the curve lies completely above x axis , which further implies co-efficient of x^2 should be greater than 0.
2) Discriminant should be less than 0.

Use the above facts and take the intersection of both the sets.

Answer 4

m>0
m< 4/61

Answer 5

(0, 4/61 )
thank u

Answer 6

glad to help. ^^

Answer 7

y=61m^2-4m is a parabola that is open upwards
when the zeros m=0 and m=4/61

So that would look like

(ugly parabola)
But we can see from this graph that y>0 when m<0 or m>4/61