Please help me with this one.

  2x^2 -x +1 = 0

Step-by-step explanation:

For roots α and β, the original equation can be factored as ...

  f(x) = 2(x -α)(x -β)

If we add 1 to each of those roots, the factors become ...

  g(x) = 2(x -(α+1))(x -(β+1))

This can be rearranged to be ...

  g(x) = 2((x -1) -α)((x -1) -β)

That is, we can get the desired equation by replacing x with x-1, effectively shifting the function right one unit.

  2(x -1)² +3(x -1) +2 = 0

  2x^2 -x +1 = 0

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.