Question

x^2-6x+9m
give m for the equation two positive solutions

Answer 1

are you just supposed to make up m?

Answer 2

Yes

Answer 3

ok. I'll let m=1, then we have
x^2-6x+9
factoring it:
(x-3)^2=0
Factors are x=3 (with a multiplicity of two).

Answer 4

ok ... this is one
than let m=0

Answer 5

ok, what do you get for m=0?

Answer 6

x^2-6x

Answer 7

ok, now factor out an x and set the whole thing equal to zero

Answer 8

solution became 0 and 6

Answer 9

yep

Answer 10

i think
in quadratic x1*x2=c/a that's mean 9m >0 m>0
and Delta -36m+36 >0 mean m > 1
that's mean that the solution is from 0 to 1

Answer 11

well, the quadratic formula will tell you the possible roots, yeah. first off, the discriminant must be larger than or equal to zero. We get,\[36-4(1)(9m)\ge0\]This gives,
\[36\ge36m\]
or,\[m \le1\]
So if m is smaller than or equal to 1, we get real roots from this quadratic. If they are to be both positive then,\[\frac{6-\sqrt{36-36m}}{2}>0\]This gives,\[6-\sqrt{36-36m}>0\]and,\[36 > 36-36m\]and,\[m>0\]This m must be BOTH greater than 0 and less than or equal to 1. Thus m is in the interval (0,1], as you said :)

Answer 12

Fine thank you ....

Answer 13

No medal for me? lol