Given the quadratic equation:
4x^2+12x+9
the zeros are found by factorizing :
4x^2+12x+9
4x^2+6x+6x+9
2x(2x+3)+3(2x+3)
=(2x+3)(2x+3)
hence the zeros are:
x=-3/2 and x=-3/2
thus
α=-3/2 and β=-3/2
thus
α-1=-3/2-1=-5/2
β-1=-3/2-1=-5/2
thus the polynomial formed by above will be having roots:
x=-5/2
x+5/2==0
hence
2x+5=0
thus the roots are:
(2x+5) and (2x+5)
the polynomials are:
(2x+5)(2x+5)
=4x^2+20x+25
