![]() ![]() Any other quadratic equation is best solved by using the Quadratic Formula. If the equation fits the form \(ax^2=k\) or \(a(x−h)^2=k\), it can easily be solved by using the Square Root Property. If the quadratic factors easily this method is very quick. Transform the equation using standard form in which one side is zero. We have solved the quadratic equation: x 2, x 32. Solving Quadratic Equations Using Factoring 1. To identify the most appropriate method to solve a quadratic equation: We have factored the quadratic equation: 2x2 + 7x + 6 (x + 2)(2x + 3) 0.if \(b^2−4ac ![]() if \(b^2−4ac=0\), the equation has 1 solution.if \(b^2−4ac>0\), the equation has 2 solutions.Using the Discriminant, \(b^2−4ac\), to Determine the Number of Solutions of a Quadratic Equationįor a quadratic equation of the form \(ax^2+bx+c=0\), \(a \ge 0\) ,.Then substitute in the values of a, b, c. Write the quadratic formula in standard form.To solve a quadratic equation using the Quadratic Formula. Solve a Quadratic Equation Using the Quadratic Formula.You see, completing the square is all about making the quadratic equation into a perfect square, engineering it, adding and subtracting from both sides so it becomes a perfect square. In the last video, we saw that these can be pretty straightforward to solve if the left-hand side is a perfect square. Quadratic Formula The solutions to a quadratic equation of the form \(ax^2+bx+c=0\), \(a \ge 0\) are given by the formula: And I put this big space here for a reason. All quadratic equations can be written in the form a x 2 + b x + c 0 where a, b and c are numbers ( a cannot be equal to 0, but b and c can be).The equation is in standard form, identify a, b, c.īecause the discriminant is negative, there are no real solutions to the equation.īecause the discriminant is positive, there are two solutions to the equation.īecause the discriminant is 0, there is one solution to the equation. This last equation is the Quadratic Formula.ĭetermine the number of solutions to each quadratic equation:
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