How to solve a quadratic equation?

 How to solve a quadratic equation?

While learning mathematics, you will often meet quadratic equations. These equations serve a mathematical way to say that a certain equation, which may resemble a real-life problem, may have more than one solution.

Identifying quadratics

The general formula of the quadratic is ax2 + bx + c = 0, but it is very rare that a quadratic equations appears in its very bare form. In exams, they often like to hide it in certain ways, for example:

·       5*cos2(x) + 3 = 2 *cos(x), where you can introduce a new variable y, and solve for y. Remember that you still need to solve for y = cos(x) after that.

·       Or basically they can use any trigonometric function or logarithm to hide a quadratic.

·       Often, a higher degree equation can be simplified to a quadratic, for example x6 + 3x3 + 2 = 0, where you can introduce a new variable, just like in the previous example.

Methods to solve a quadratic

The general formula for solving the quadratic is x = (-B + or – SQRT(B2 – 4AC))/2A

Where A, B,C are the coefficients of the equations. If you don’t know what a coefficient is, it is basically the number before the unknowns in the equation. Often you see can see that e.g. x2 doesn’t have a number before it, but that simply means that its coefficient is 1.

Also, you can use the Vieta-formulas to solve a quadratic, which are relationships between the coefficients of the equation and its roots (solutions).

-B/A = the two roots added together

C/A = the two roots multiplied together

I recommend that you get comfortable with these relationships, because these Vieta-formulas in some way remain true at higher degree equations.

Another method to solve a quadratic is, completing the square, for example x2 + 2x + 1 = (x+1)2, so we can know that -1 is the only solution to our quadratic equation.

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