Introduction of Quadratic Equation

We will discuss about the introduction of quadratic equation.

A polynomial of second degree is generally called a quadratic polynomial.

If f(x) is a quadratic polynomial, then f(x) = 0 is called a quadratic equation.

An equation in one unknown quantity in the form ax\(^{2}\) + bx + c = 0 is called quadratic equation.

A quadratic equation is an equation of the second degree.        

The general form of a quadratic equation is ax\(^{2}\) + bx + c = 0 where a, b, c are real numbers (constants) and a ≠ 0, while b and c may be zero.

Here, x is the variable, a is called the coefficient of x\(^{2}\), b the coefficient of x and c the constant (or absolute) term.

The values of x which satisfy the equation are called the roots of the quadratic equation.


Examples of quadratic equation:

(i) 5x\(^{2}\) + 3x + 2 = 0 is an quadratic equation.

Here, a = the coefficient of x\(^{2}\) = 5,

b = coefficient of x = 3 and

c = constant = 2


(ii) 2m\(^{2}\) - 5 = 0 is an quadratic equation.

Here, a = the coefficient of m\(^{2}\) = 2,

b = coefficient of m = 0 and

c = constant = -5


(iii) (x - 2)(x - 1) = 0 is an quadratic equation.

(x - 2)(x - 1) = 0

⇒ x\(^{2}\) - 3x + 2 = 0

Here, a = the coefficient of x\(^{2}\) = 1,

b = coefficient of x = -3 and

c = constant = 2


(iv) x\(^{2}\) = 1 is an quadratic equation.

x\(^{2}\) = 1

⇒ x\(^{2}\) - 1 = 0

Here, a = the coefficient of x\(^{2}\) = 1,

b = coefficient of x = 0 and

c = constant = -1


(v) p\(^{2}\) - 4p + 4 = 0 is an quadratic equation.

Here, a = the coefficient of p\(^{2}\) = 1,

b = coefficient of p = -4 and

c = constant = 4






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