Question

Please help me find the roots of following polynomial equation:
e^2x-5(e^2x)+6 = 0

Answer 1

is that a typo? I dont think there is a '2' in the middle term..

Answer 2

Its not a typo.Its from our exam paper.

Answer 3

@amistre64...May you please,please,please see my problem? Please??????? :)

Answer 4

then combine like terms ..... a = e^2x

-4a+6 = 0

a = 6/4 = 3/2

e^2x = 3/2

2x = ln(3/2)

x = ln(3/2)/2

Answer 5

if i can find it ;)

Answer 6

perhaps it is in my profile...try 2 click once there :)

Answer 7

I am not getting your solution. Can you please explain?

Answer 8

not getting as you dont follow it? or the answer is wrong?

Answer 9

I do not follow it.Its kinda tough.

Answer 10

pleasse come back later to my question, dont quite understand what you mean

Answer 11

e^2x can be substituted for becasue it doesnt change in the problem; its an unknown that we determine; so to clean up the equation, make it = a and use 'a' instead.

a -5a +6 =0

-4a +6 = 0

-4a = -6

a = -6/-4 = 6/4 = 3/2

Answer 12

ok :)

Answer 13

since e^2x = a ; we told it to ...

e^2x = 3/2

we solve for x by using logarithmic properties..

ln(e^2x) = ln(3/2)

2x = ln(3/2)

x = ln(3/2)
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2

Answer 14

Its involved I guess.I would look into it.Thanks for your help.I appreciate it.

Answer 15

your welcome

But I really think that this could have been a typo; which would make this part easier:

a = e^x

a^2 -5a +6 = 0

(a-6)(a+1) = 0

a = 6 and a = -1

e^x = a

e^x = 6 ; x = ln(6)
e^x = -1, which is impossible so disregard the -1

x = ln(6)