General Rule
If the Polynomial is of degree n, then it has n zeroes, then it cuts x axis at n points.
Now, explaining the above rule
→If a polynomial has single zero, then it cuts x axis at one point, which will be linear function ,like , x=a.
→If the polynomial cuts x axis at two points, it means it has two zeroes ,which will be a quadratic function.
→Like wise, Polynomial of third degree cuts x axis at three points and it will be a cubic polynomial.
How Zeros of a polynomial function used to create a graph
⇒Now, suppose the two zeroes of function are ,a and b.
x=a and x=b.That is, x-a=0 and x-b=0
To Obtain the function, multiply the two linear function
(x-a)(x-b)=0
Which gives a Quadratic function.
→x² -(a+b)x+ab=0
⇒Similarly, for three roots (a,b,c) of the function,the function will be
→x³-(a+b+c)x²+(ab+bc+ca)x²-abcx+k(Constant)=0
Which will be a Cubic function.
