Quadratic Equation

Maths Course Class VIII Maths: Algebra Quadratic Equation

Quadratic Equation Video In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as^[1]

{displaystyle ax^{2}+bx+c=0,,}

where $x$ represents an unknown value, and $a$ , $b$ , and $c$ represent known numbers, where $a \neq 0$ . (If $a = 0$ and $b \neq 0$ then the equation is linear, not quadratic.) The numbers $a$ , $b$ , and $c$ are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term. The values of $x$ that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation^[3]

{displaystyle ax^{2}+bx+c=a(x-r)(x-s)=0}

where $r$ and $s$ are the solutions for $x$ .

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