Question - Quadratic Equation Solution Using the Quadratic Formula
Solution:
The provided image shows the quadratic formula, which is used to find the solutions of a quadratic equation $$ ax^2 + bx + c = 0 $$. The solutions using the quadratic formula are:\[ x = \frac{{-b \pm \sqrt{b^2 - 4ac}}}{{2a}} \]This formula calculates the roots of any quadratic equation where $$ a \neq 0 $$. The term inside the square root, $$ b^2 - 4ac $$, is known as the discriminant, and it determines the nature of the roots:- If $$ b^2 - 4ac > 0 $$, there are two distinct real roots.- If $$ b^2 - 4ac = 0 $$, there is one real root (a repeated root).- If $$ b^2 - 4ac < 0 $$, there are two complex roots.To solve a specific quadratic equation using this formula, one should substitute the values of $$ a $$, $$ b $$, and $$ c $$ from the equation into the formula and simplify.
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