#Quadratic #Equations – #Mathematics Class 10 #CBSE | Part 1 | Sameer Kohli

Introduction to the topic –

In algebra, a quadratic (from the Latin quadratus for “square”) is an equation having the form

+bx+c=0,} +bx+c=0,}

where x represents an unknown, and a, b, and c represent better-known numbers, with a ≠ 0.

If a = 0, then the equation is linear, not quadratic, as there is no } ax^2 term.

The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient, and the constant

or free term.[1]

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of its left-hand side. A quadratic equation has at most two solutions.

If there’s no real answer, there are two complex solutions.

If there is only one solution, one says that it is a double root. So a quadratic equation has always two roots, if complex roots are considered, and if a double root is counted for two. If the two solutions are denoted r and s (possibly equal), one has

+bx+c=a(x-r)(x-s).} +bx+c=a(x-r)(x-s).}

Thus, the process of solving a quadratic equation is also called factorizing or factoring. Completing the square is the standard method for that, which results in the quadratic formula, which expresses the solutions in terms of a, b, and c. Graphing may also be used for getting an approximate value of the solutions. Solutions to problems that may be expressed in terms of quadratic equations were known as early as 2000 BC.

Because quadratic involves just one unknown, it is called “univariate”.

The quadratic solely contains powers of x that are non-negative integers, and therefore it is a polynomial equation.

In specific, it’s a second-degree polynomial equation, since the greatest power is 2.

The solutions of the quadratic equation ax2 + bx + c = 0 correspond to the roots of the function f(x) = ax2 + bx + c, since they are the values of x for which f(x) = 0.

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