16. Is x = √7 − 9 a quadratic equation? Simplify and check.
Answers
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✨We saw that quadratic equations can represent many real-life situations. Now that we know what quadratic equations are, let us learn about the different methods to solve them. Here we will try to develop the Quadratic Equation Formula and other methods of solving the quadratic equations.✨
✨Methods of Solving Quadratic Equations✨
There are three main methods for solving quadratic equations:
- Factorization
- Completing the square method
- Quadratic Equation Formula
In addition to the three methods discussed here, we also have a graphical method. As you may have guessed, it involves plotting the given equation for various values of x. The intersection of the curves thus obtained with the real axis will give us the solutions.
✨Factorization✨
The first and simplest method of solving quadratic equations is the factorization method. Certain quadratic equations can be factorised. These factors, if done correctly will give two linear equations in x. Hence, from these equations, we get the value of x.
✨Completing the Square Method✨
Each quadratic equation has a square term. If we could get two square terms on two sides of the quality sign, we will again get a linear equation.
✨Quadratic Equation Formula✨
There are equations that can’t be reduced using the above two methods. For such equations, a more powerful method is required. A method that will work for every quadratic equation. This is the general quadratic equation formula. We define it as follows: If ax2 + bx + c = 0 is a quadratic equation, then the value of x is given by the following formula.
Just plug in the values of a, b and c, and do the calculations. The quantity in the square root is called the discriminant or D. The below image illustrates the best use of a quadratic equation.
