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
11 and 12 Grade Math
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