Uploaded December 2018 | Updated September 2026, 2 weeks ago
In the previous lecture we showed how any quadratic equation can be solved by "completing the square". We also showed geometrically that any general form quadratic expression "x-squared + bx + c" where c has a value of "(b/2) squared" is a perfect square, However, this geometric proof assumed that all the terms in the quadratic are positive. The x-squared and constant terms must be positive since they are squared, but what does this proof look like if the bx term is negative? We also demonstrate how solutions to quadratic equations can be calculated when the constants in the quadratic are irrational.
In the previous lecture we showed how any quadratic equation can be solved by "completing the square". We also showed geometrically that any general form quadratic expression "x-squared + bx + c" where c has a value of "(b/2) squared" is a perfect square, However, this geometric proof assumed that all the terms in the quadratic are positive. The x-squared and constant terms must be positive since they are squared, but what does this proof look like if the bx term is negative? We also demonstrate how solutions to quadratic equations can be calculated when the constants in the quadratic are irrational.
