Answer:
- a = 2/3
- b = 2/3
- c = -14 1/3 = -43/3
Explanation:
You want the coefficients of the given quadratic equation when it is written in general form.
General form
The general form of a quadratic equation in one variable is ...
ax² +bx +c = 0
We can expand the given equation and subtract the right side constant to give this form.
2/3(x -4)(x +5) = 1
2/3(x² -4x +5x -20) = 1
2/3x² +2/3x -2/3(20) -1 = 0
2/3x² +2/3x -(14 1/3) = 0
The values of a, b, c are ...
- a = 2/3
- b = 2/3
- c = -14 1/3
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Additional comment
It is often convenient for the coefficients to have mutually prime integer values. We can multiply the given coefficients by 3 to achieve that condition:
2x² +2x -43 = 0 . . . . . . a = 2; b = 2; c = -43
The graph of this will have the same x-intercepts as the above equation, but will be stretched vertically by a factor of 3.
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