the function is: f(x)=1/2x^2+5/2x-3/2 find the following a) find the zeros of th

Question

the function is: f(x)=1/2x^2+5/2x-3/2

find the following
a) find the zeros of the function
b)write in factored form
c)write in completely factored form

please show work
thanks

Explanation / Answer

A)Find zeros -> f(x)= 0 0=1/2x^2+5/2x-3/2, multiply both sides by 2 -> x^2+5x-3=0 then complete the square to get -> x^2+5x+6-6-3=0 ->(x+2)(x+3)-6-3=0 -> (x+2)(x+3)=9 -> x+2=9 or x+3=9 x=7 or x=6 i just thought of 2 numbers that added up to be 5 (2+3=5), multiplied the two numbers (2*3=6) and added and subtracted that number (6) from the equation so as not to change anything (6-6=0) B) I'm assuming the factored form is f(x)=1/2*(x^2+5x-3) C) f(x)=1/2*[(x+2)(x+3)-9] -> completely factored form (see above on how to derive)

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