Answer:
The factors of the quadratic equation are (x+3/2) and (x+3/2) simultaneously.
Step-by-step explanation:
A simple way to find the factor is to use Bhaskara which gives us the roots of the quadratic equation:
[tex]R1,R2=(-b+-sqrt(b^2-4.a.c)) / 2.a[tex] ()
Where a is the quadratic term coefficient, b is the linear term coefficient and is the independent term. By calculating the roots the factorized quadratic equation will be:
[tex]a(x-R1)(x-R2)[/tex]
In the equation (x-R1) and (x-R2) are the two factors of the equation.
In our example the coefficients are:
a=4
b=12
c=9
Therefore:
[tex]R1,R2=(-12+-sqrt(12^2-4.4.9)) / 2.4[tex]
[tex]R1,R2=(-12+-sqrt(144-144)) / 2.4[tex]
[tex]R1,R2=(-12+-sqrt(0)) / 8[tex]
[tex]R1,R2=(-12)/8=-3/2[tex]
Notice that -3/4 is R1 and R2, that is, the roots are equals. By replacing in the factorized form we have:
[tex]4(x-(-3/2))(x-(-3/2))[/tex]
[tex]4(x+3/2)(x+3/2)[/tex]
