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It does not matter what value we have for a.
We can plug this into the quadratic formula and keep the variable a as part of our answer.
`(-b +- sqrt(b^2 - 4ac))/(2a)`
where a, b and c are
`ax^2 + bx + c`
in the case of our problem
`y = ax^2 + 3x - 2`
`a = a`
`b = 3`
`c = -2`
So we plug those values into our quadratic formula
`(-3 +- sqrt(3^2 - 4*a*(-2)))/(2a)`
These are our two solutions. One plus, one minus.
`x = (-3 + sqrt(9 + 8a))/(2a)`
`x = (-3 - sqrt(9 + 8a))/(2a)`
If 9+8a is less than zero, the square root will have an imaginary solution, and so there will be no real solutions to this problem.
This equation cannot be solved by graphing unless the value of a is known, so the following answer is given assuming the given function is `y = 2x^2 + 3x - 2 ` and the equation needed to be solved is `2x^2 + 3x - 2 = 0 ` .
This is a quadratic function, and its graph is a parabola:
The solutions of the equation are the x-coordinates of the points where the graph intersects x-axis. As can be seen from the graph, these points are (-2,0) and (0.5, 0), so the solutions of the equation are x = -2 and x = 0.5
This can be checked by plugging these values back into the equation and verifying that they yield 0:
` 2*(-2)^2 + 3(-2) - 2 =8 - 6 - 2 = 0 `
`2*(0.5)^2 + 3*0.5 - 2 = 0.5 + 1.5 - 2 = 0 `
So the solutions are x = -2 and x = 0.5.
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