By how much does the larger root of the equation 2b^2+5b = 12 exceed the smaller root?  Choose the most appropriate option.
A) 5 / 2 B) 10 / 3 C) 7 / 2 D) 14 / 3 E) 11 / 2

Rationale: "for 2 b ^ 2 + 5 b = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: E