(x-3)%3D(x%2B5)(x-1)-is-a-quadratic-equation-or-not.jpeg "(2x-1)(x-3)=(x+5)(x-1) Is A Quadratic Equation Or Not")
Is (2x-1)(x-3)=(x+5)(x-1) a Quadratic Equation?
A quadratic equation is an equation that can be written in the standard form:
ax² + bx + c = 0
where a, b, and c are constants and a ≠ 0.
Let's analyze the given equation: (2x-1)(x-3) = (x+5)(x-1).
To determine if it's a quadratic equation, we need to simplify it and see if it can be written in the standard form.
Simplifying the Equation
First, we expand both sides of the equation using the distributive property (or FOIL method):
- (2x-1)(x-3) = 2x² - 6x - x + 3 = 2x² - 7x + 3
- (x+5)(x-1) = x² - x + 5x - 5 = x² + 4x - 5
Now, the equation becomes: 2x² - 7x + 3 = x² + 4x - 5
Rearranging to Standard Form
Next, we move all terms to one side of the equation to get a zero on the other side:
2x² - 7x + 3 - x² - 4x + 5 = 0
Combining like terms, we get:
x² - 11x + 8 = 0
Conclusion
The simplified equation x² - 11x + 8 = 0 is in the standard form of a quadratic equation (ax² + bx + c = 0). Therefore, the equation (2x-1)(x-3) = (x+5)(x-1) is a quadratic equation.