Framing a Quadratic Equation

Quadratic equation:

A quadratic equation is an equation with degree (highest power) 2.

Example:

i)                    x² + 5x + 6 = 0;

ii)                   x² – x – 6 = 0.

Root or solution:

A root (a solution) of a quadratic equation is a value which satisfies the equation.

Example:

i)                    -3 is a root of x² + 5x + 6 = 0.

iii)                 3 is a root of x² – x – 6 = 0.

Factor:

If ‘a’ is a root of quadratic equation then x-a is a factor to it.

Example:

Since 3 is a root of x² – x – 6 = 0, x-3 is a factor to it.

Framing a quadratic equation:

If ‘a’ and ‘b’ are the roots of a quadratic equation then x-a and x-b are its corresponding factors.

So, the corresponding equation is,

(x-a)(x-b)=0

x² –(a+b)x + ab = 0.

Example:

Frame a quadratic equation with the roots 1 and 2.

Solution:

Here a=1 and b=2.

So the corresponding equation is,

x² –(a+b)x + ab = 0

x² –(1+2)x + 1*2 = 0

x² –3x+2=0.