Question

Give some unknown formulas related to Quadratic Equation.

Answer 1

Hey there,

Some unknown formulas

*Symmetric function of the roots

Symmetric function of the roots of an eqn is a function in which all the roots are involved alike ,so that expression remains same

I.E Let the expression a+b+y,ab+by+ya ,any are symmetric function of a,b,y

Then, summation of a=a+b+y

Summation of ab=ab+by+ya

No. Of terms in symmetric function=n!/(n-a)!b! ,
Where ,

n=total no of roots of eqn

a=total no of roots in symmetric function

b=no. Of roots having same degree

There are many but it's difficult to write for each these.

Hope it helps

Answer 2

[x-(a)][x-(b)]<0      X lies between a and b
[x-(a)][x-(b)]<=0    X lies from a and b
[x-(a)][x-(b)]>0      X lies between (-∞ to a) and ( b to ∞)
[x-(a)][x-(b)]>=0    X lies between (-∞ to a) and ( b to ∞) including a and b
 
This is the case when (a)<(b).