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Find the values of m so that the expression x 2 -5mx+4m 2 +1 is always positive for real values of x. Please answer this problem as soon as possible.

Find the values of m so that the expression x2-5mx+4m2+1 is always positive for real values of x.
 
Please answer this problem as soon as possible.

Grade:11

1 Answers

Susmita
425 Points
5 years ago
Whenever u get a problem like this try to write in whole square form.
x2-5mx+4m2+1
=x^2 -2.x.\frac{5m}{2}+(\frac{5m}{2})^2-(\frac{5m}{2})^2 +4m^2 +1=(x -\frac{5m}{2})^2-(\frac{5m}{2})^2 +4m^2 +1
=(x -\frac{5m}{2})^2+1-\frac{9m^2}{4}
So for it to be always positive
1-\frac{9m^2}{4}=0
Or,m=\pm \frac{2}{3}
Please approve if you are help.thank you.
 

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