The curve which represents a quadratic polynomial meets the axis at (2,0) and (-2,0). Find the quadratic polynomial.

Problem : The curve which represents a quadratic polynomial meets the axis at (2,0) and (-2,0). Find the quadratic polynomial.

Doubt by Muskan

Solution : 
We know the graph / curve of the quadratic polynomial when plotted then it cuts the axes at its zeros.

So we can say that 2 and -2 are the zeroes of the polynomial.

Let α = 2 and β = -2

So  the required quadratic polynomial will be
p(x) = x² - (α+β)x + αβ
p(x) = x² - [2+(-2)]x + (2)(-2)
p(x) = x² - 0x -4
p(x) = x² - 4

which is the required polynomial.