Question

Find a quadratic equation having the given numbers as solutions. x= -1/2, x=9/2. Answer must be in ax^2+bx+c=0. a>0 and a,b,c do not all have a common factor

Answer 1

sols x=-1/2 and x=9/2, so ax^2+bx+c=(x+1/2)(x-9/2)=0
(x+1/2)(x-9/2)
=x^2 + 1/2x - 9/2x -9/4
=x^2 - 4x -9/4

so we can see a=1, b=-4, c=-9/4

Answer 2

wow, this is very confusing!!

Answer 3

you have your quadratic equation there right? so a quadratic equation can be factorised into the form of (x+a)(x+b)=0 (eq1) where solutions are -a and -b
so you have there -a=-1/2, a=1/2 and -b=9/2, b=-9/2
apply this into (eq1) we get (x+1/2)(x-9/2)=0
expand this you will get another equation in form of ax^2 + bx + c =0 (*)
in this case your expansion equation is x^2 - 4x -9/4 = 0 (**)
compare (*) and (**) you can see a=1, b=-4, c=-9/4