(2x-1)(x-3)=(x+5)(x-1) Is A Quadratic Equation

Jasonbradley

2 min read

·

Jun 16, 2024

46

Share

Is (2x-1)(x-3)=(x+5)(x-1) a Quadratic Equation?

Let's investigate whether the equation (2x-1)(x-3) = (x+5)(x-1) is a quadratic equation.

Understanding Quadratic Equations

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants, and a is not equal to zero. The highest power of the variable x in a quadratic equation is 2.

Analyzing the Given Equation

1. Expand both sides:

   • (2x-1)(x-3) = 2x² - 7x + 3
   • (x+5)(x-1) = x² + 4x - 5

2. Rewrite the equation:

   • 2x² - 7x + 3 = x² + 4x - 5

3. Simplify by moving all terms to one side:

   • 2x² - 7x + 3 - x² - 4x + 5 = 0
   • x² - 11x + 8 = 0

Conclusion

We have successfully rewritten the equation in the standard quadratic form ax² + bx + c = 0, where a = 1, b = -11, and c = 8.

Therefore, (2x-1)(x-3) = (x+5)(x-1) is indeed a quadratic equation.