Factorising a Quadratic Equations

Topic : Quadratic Equations

Questions : Explain the procedure involved during Factorisation of Quadratic Equation.

Solution :

The general form of a quadratic equation is :
ax² + bx + c = 0
In order to factor this we need to find two numbers such that, the sum of those two numbers is b, which is the co-efficient of the middle term and the product of those two numbers is ac, where a is the co-efficient of leading term and c is called the constant term.

Suppose, the two numbers are p and q
then p + q = b
and pq = ac

ax² + bx + c = ax² + (p + q)x + pq/a
= (ax² + px) + (qx + pq/a)
= ax(x + p/a) + q (x + p/a)
= (ax + q) + (x + p/a)

Hope the method of how to solve a quadratic equation helps you to solve number of questions like this.

Question to Find the Area of Region

Topic : Area of the Region

Question : Find the area of the region obtained by the intersection of a plane perpendicular to x-axis and passing through(2,0,0) with 2x^2+3y^2+4z^2=24.

Answer :

Putting x=2 in the equation
gives us 3y^2+4z^2=16
get this in to ellipse standard form
and use Pi*a*b
to get 8pi/sqrt(3).

Hope the hint will help you to solve the problem easily.