If α and β are the zeroes of 4x2 + 12x + 9, form a quadratic polynomial whose zeroes are α-1 and β-1

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