Which quadratic equation

Then substitute 1 which is understood to be in front of the x 2 , —5, and 6 for a , b , and c, respectively, in the quadratic formula and simplify. Because the discriminant b 2 — 4 ac is positive, you get two different real roots.

Example produces rational roots. In Example , the quadratic formula is used to solve an equation whose roots are not rational. Then substitute 1, 2, and —2 for a , b , and c, respectively, in the quadratic formula and simplify. Since the discriminant b 2 — 4 ac is 0, the equation has one root. The quadratic formula can also be used to solve quadratic equations whose roots are imaginary numbers, that is, they have no solution in the real number system.

Since the discriminant b 2 — 4 ac is negative, this equation has no solution in the real number system. But if you were to express the solution using imaginary numbers, the solutions would be. A third method of solving quadratic equations that works with both real and imaginary roots is called completing the square. Using the value of b from this new equation, add to both sides of the equation to form a perfect square on the left side of the equation.

Add or to both sides. There is no solution in the real number system. Previous Quiz Solving Quadratic Equations. Next Word Problems. Removing book from your Reading List will also remove any bookmarked pages associated with this title. Are you sure you want to remove bookConfirmation and any corresponding bookmarks? My Preferences My Reading List. Keep reading for examples of quadratic equations in standard and non-standard forms, as well as a list of quadratic equation terms.

The easiest way to learn quadratic equations is to start in standard form. While not every quadratic equation you see will be in this form, it's still helpful to see examples.

Keep in mind that the first constant a cannot be a zero. As you develop your algebra skills, you'll find that not every quadratic equation is in the standard form. Check out examples of several different instances of non-standard quadratic equations. Sometimes a quadratic equation doesn't have the linear coefficient or the bx part of the equation. Examples include:.

Factoring is one way to solve a quadratic equation. Here are examples of quadratic equations in factored form:. If you'd like a little more explanation on quadratic equations, check out a list of essential math vocabulary terms. They can help you understand more about quadratic equations, what they're for and how to solve them.