Question

Find all the solutions to the question x^2e^x-3xe^x+2e^x=0

Answer 1

x^2e^x-3xe^x+2e^x=0

Factorize the e^x

e^x ( x^2 - 3x + 2 ) = 0

Factorize the trionomial x^2 - 3x + 2

e^x ( x - 2) (x - 1) =0

Then use the zero factor theorem if e^x ( x - 2) (x - 1) =0, then ( x - 2) =0 or (x - 1) =0

Solve for x

( x - 2) =0

x = 2

(x - 1) = 0

x = 1

So the solution is x = 2 and x = 1