solve the equations 2X^2=X+3 by graphing. If an exact value for the root(s) cannot be found, state the consecutive integers between which the root(s) is located.
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One equation is y = x + 3. (2x - 3)(x + 1)
Plot a point at (0,3) and make a line through that point that has a slope of 1. This should pass through
a point at (-3,0). Plot a point at (0,0), which will be the vertex of y = 2 x^2.
To the left the vertex, figure out what y equals if you plug in -1 as x in 2 x^2. You would get y = 2 when x = -1. The point (-1,2) is on the line y = x+3, so 3 is a root. To the right of the vertex, you can figure out that (1,2) and (2,8) are points of the parabola. The line will pass between these points, and if you set x equal to 1.5, you will get (1.5,4.5) as a point of the parabola, which is also a point of the line. So the two roots are -1 and 1.5.
Plot a point at (0,3) and make a line through that point that has a slope of 1. This should pass through
a point at (-3,0). Plot a point at (0,0), which will be the vertex of y = 2 x^2.
To the left the vertex, figure out what y equals if you plug in -1 as x in 2 x^2. You would get y = 2 when x = -1. The point (-1,2) is on the line y = x+3, so 3 is a root. To the right of the vertex, you can figure out that (1,2) and (2,8) are points of the parabola. The line will pass between these points, and if you set x equal to 1.5, you will get (1.5,4.5) as a point of the parabola, which is also a point of the line. So the two roots are -1 and 1.5.
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2x ² = x + 3
2x ² - x - 3 = 0
( 2x - 3 ) ( x + 1 ) = 0
2x - 3 = 0 .......... & ........... x + 1 = 0
2x = 3 .......... & ........... x = -1
x = 3/2 .......... & ........... x = -1
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2x ² - x - 3 = 0
( 2x - 3 ) ( x + 1 ) = 0
2x - 3 = 0 .......... & ........... x + 1 = 0
2x = 3 .......... & ........... x = -1
x = 3/2 .......... & ........... x = -1
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is it 2(X^2) or (2X)^2 ?