Question

For what positive values of 'm' roots of the the following equations are (a) equal (b) distinct (c) imaginary 1 )a┬▓-ma+1=0. 2) x┬▓-mx+9=0 3) r┬▓-(m+1)r+4=0

Answer 1

1)discriminant=m^2 - 4
    (a) discriminant=0, i.e. m=2 (because m is positive)
    (b) discriminant>0, i.e. m>2
    (c) discriminant<0, i.e. m>0 and m<2 

2)discriminant=m^2 - 36
    (a) discriminant=0, i.e. m=6 (because m is positive)
    (b) discriminant>0, i.e. m>6
    (c) discriminant<0, i.e. m>0 and m<6

3)discriminant=(m+1)^2 - 16
    (a) discriminant=0, i.e. m+1=4 =>m=3 (because m is positive)
    (b) discriminant>0, i.e. m+1>4 =>m>3
    (c) discriminant<0, i.e. m>0 and m+1<4 => m>0 and m<3