IIT JEE Quadratic Equations

I want some sample Quadratic Equations questions for preparation of IIT Joint Entrance exam JEE so can you provide me?

[pawan]

Ok, as you want the some sample Quadratic Equations questions of IIT Joint Entrance exam JEE so here I am providing you.

IIT JEE exam Quadratic Equations questions

Quadratic equations are those equations which can be written in the form f(x)=0 where f(x) is a second degree polynomial. General form of a Quadratic equation is: ax2+bx+c=0 (a is not equal to 0); and solving for x gives
x = (-b + √D ) / 2a
and
x = (-b - √D ) / 2a

Where D is the Discriminant and D = b2-4ac

The Discriminant
The term b2-4ac is called the Discriminant, and is denoted usually by the symbol ∆ or the letter ‘D’.

Roots of a Quadratic Equation : Are they real/unreal, equal or unequal ?
If D>0, the equation has real and unequal roots, if D=0, the equation has real and equal roots (also called real repeated roots), and if D<0, the equation has unreal roots, occurring as conjugate pairs. That is if one root is of
the form u+iv, the other root would be u-iv. If α and β are roots of a Quadratic equation, then
o The equation can be written as : a(x-α)(x-β)=0
o The equation could also be written as x-(α+β)+αβ=0

Using Substitution to convert equations to Quadratic Form
A Quadratic equation could be solved by factorization, or by using the direct formula written above. Certain equations are not quadratic, but can be reduced to a quadratic form by certaing substitutions. In such cases, applying the right form of substitution yields the required solutions.

Example :
ax4+bx2+c=0; substitute x2=y, to form a quadratic equation in y.
3x+√x-2=0; substitute √x=y to form a quadratic equation in y.
x+√(x-4)=4; transport x to RHS and then square both sides to get a quadratic equation.

Remember, when using substitutions, be sure that you solve for the original variable, and that the solution does not violate any constraints. For instance, if you have √(x-1) in the original equation, then x has to be greater than 1, as square root cannot be negative.
Also, if you have a step like: (x-z)(f(x))=(x-z)(g(x)) then, instead of just dividing both sides by (x-z), you write x=z as one of the solutions.

Dealing with Cubic and Higher Order Equations
A cubic equation is of the form f(x)=0, where f(x) is a degree 3 polynomial. The general form of a cubic equation is ax3+bx2+cx+d=0, where a is not equal to 0. If α, β, γ are roots of the equation, then equation could be written as:
a(x-α)(x-β)(x-γ)=0, or also as
x3-(α+β+γ)x2+(αβ+βγ+γα)x-(αβγ)=0
Thus, we have
α+β+γ=-b/a
αβ+βγ+γα=c/a
αβγ=-d/a
A quadratic equation may have all repeated real roots, two repeated and one distinct real root,
one distinct real and two conjugate unreal roots, all distinct real roots.

For more questions here is the attachment