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Quadratic Equations |

Quadratic Equation

An equation of the form ax2+ bx + c = 0, where a, b, c are real numbers and a 0, is called a quadratic equation in x.

Any equation of the form p(x) = 0, where p(x) is polynomial of degree 2, is a quadratic equation.

But when we write the terms of p(x) in descending order of their degrees, then we get the standard form of the equation.

That is, , standard form of a quadratic equation and

That is, ax2+ bx + c = 0,  a ≠ 0 is called the standard form of a quadratic equation and

 

y = ax2+ bx + c   is called a quadratic function.

 

A quadratic equation has
maximum two  roots.

A real number α is called a root of the
quadratic equation ax2+ bx + c = 0, a ≠ 0,

                 if aα2+ bα + c = 0,

v Any quadratic equation can have at most two roots.

Note : If α is a root of ax2+ bx + c = 0, then we say that

(i) x = α satisfies the equation ax2+ bx + c = 0  or

  (ii) x = α is a solution of the equation ax2+ bx + c = 0

The roots of a quadratic equation ax2+ bx + c = 0 are called the zeros of the polynomial ax2+ bx + c 

Solving a quadratic equation means finding its roots.

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