Find a quadratic equation that has the solution set (4/3, 2).
x = x = 2
3x = 4 x = 2
3x - 4 = 0 x - 2 = 0
(3x - 4)(x - 2) = 0
3x2 - 10x + 8 = 0
Please notice that this is simply the exact reverse of
the step by step procedure for solving the resulting
equation, which would be
3x2 - 10x + 8 = 0
(3x - 4)(x - 2) = 0
3x - 4 = 0 x - 2 = 0
3x = 4 x = 2
x = x = 2
And...
A rectangular picture is 8 by 10 inches. The frame has the same width all the way around. The frame and the picture together have a total area of 168 square inches. What is the width of the frame.
here is the picture and frame:
Let the width of the frame be x
Draw in the 4 square corners, each of which has
side of length x, the width of the frame:
The total bottom width of the framed picture is gotten by adding
the green dimensions across the bottom
x + 8 + x or 2x + 8
The total height of the framed picture is gotten by adding
the green dimensions along the right edge:
x + 10 + x or 2x + 10
Using the formula
Area = (bottom width) times (vertical height) we have the equation:
168 = (2x + 8)(2x + 10)
Do you know how to simplify and solve that equation?
If not post again asking how to solve it. The
solutions you get are x = 2 and x = -11.
We ignore the negative solution and conclude that
the frame is 2 inches wide.
Edwin