Page 3 - 10-Math-1 QUADRATIC EQUATIONS

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1.1. Quadratic Equation Version 1.1

An equation, which contains the square of the unknown (variable)
quantity, but no higher power, is called a quadratic equation or an
equation of the second degree.
A second degree equation in one variable x of the form
ax2 + bx + c = 0, where a m 0 and a, b, c are real numbers, is called
the general or standard form of a quadratic equation.
Here a is the co-efficient of x2, b is the co-efficient of x and constant
term is c.

Remember that: If a = 0 in ax2 + bx + c = 0, then it reduces to a
linear equation bx + c = 0.

The equations x2 - 7x + 6 = 0 and 3x2 + 4x = 5 are the examples of
quadratic equations. x2 - 7x + 6 = 0 is in standard form but
3x2+ 4x= 5 is not in standard form. If b = 0 in a quadratic equation
ax2 + bx + c = 0, then it is called a pure quadratic equation. For
example x2 - 16 = 0 and 4x2 = 7 are the pure quadratic equations.

Activity: Write two pure quadratic equations.

1.2 Solution of quadratic equations

To find solution set of a quadratic equation, following methods
are used:
(i) factorization (ii) completing square

1.2(i) Solution by factorization:

In this method, write the quadratic equation in the standard form
as ax2 + bx + c = 0. If two numbers r and s can be found for equation
(i) such that r + s = b and rs = ac, then ax2 + bx + c can be factorized
into two linear factors. The procedure is explained in the following
examples.

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