Quadratic equation solution
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If we apply the -formule we immediately notice that: Note that the solution can also be found by applying the following special product:Īpplying this formula in the equation above we notice that en. The equation has two coinciding solutions, sometimes it is said that the equation has just one solution. Use the square root property to find the square root of. Transform the equation so that a perfect square is on one side and a constant is on the other side of the equation. In this case it is not easy to use factorizing ( and if you would divide both sides by you get fractions as coefficients). This method is used if the form of the equation is: or (where represents a constant) Steps to solve quadratic equations by the square root property: 1. If this method does not give the results sufficiently fast, then you would apply the -formula.
![quadratic equation solution quadratic equation solution](https://i.ytimg.com/vi/5ieiYdauH1M/maxresdefault.jpg)
When do we use the -formula? When you have enough skills to try the factorizing method you would prefer this although you know this will not always help you. We notice immediately that the left-hand side can be factorized:įor comparison, we also solve this equation with the -formula: It is used to solve real-life situations. In this case the equation has no real solutions and then we say that the equation has no solutions. Polynomial of type ax2 +bx+c, when equated to zero, gives a Quadratic equation. In this case the solutions and are equal and then we say that the equation has just one solution (actually 2 coinciding solutions). In this case the solutions and are different and then we say that the equation has two solutions. This depends on the value of the discriminant, i.e.
![quadratic equation solution quadratic equation solution](https://i.ytimg.com/vi/T0Ark8OuwWo/hqdefault.jpg)
We already mentioned that there are at most two solutions. Here we have used the notation, but we can also write: Solving a quadratic equation gives two (real) solutions at most: or : On the other hand a solution is guaranteed. If you do not have the skills or if you do not want to apply this method there is another approach which always works and which is widely known as the -formula. However, this method is not always possible and also requires some skills. The advantage of that method is that it may provide a solution rapidly. In Quadratic equations (factorizing) we have explained under which conditions we can solve a quadratic equation by factorizing. The solutions of the quadratic equation a x 2 + b x + c 0 are given by the quadratic formula: Note. Of course we have, because otherwise the equation would not be quadratic but linear. Solving quadratic equations by quadratic formula. Any other quadratic equation is best solved by using the Quadratic Formula.A quadratic equation has the following general form: 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.