Answer:
d. Two complex solutions
Step-by-step explanation:
We have been given a trinomial [tex]2x^2+4x+4[/tex] and we are supposed to predict the type of solutions of our given trinomial.
We will use discriminant formula to solve for our given problem.
[tex]\text{Discriminant}=b^2-4ac[/tex], where,
[tex]a =\text{Coefficient of }x^2[/tex],
[tex]b =\text{Coefficient of }x[/tex],
[tex]c =\text{Constant }[/tex]
Conclusion from the result of Discriminant are:
[tex]D<0\text{ means two complex zeroes}[/tex]
[tex]D=0\text{ means one real zero with of multiplicity two}[/tex]
[tex]D>0\text{ means two distinct zeroes}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Discriminant}=4^2-4*2*4[/tex]
[tex]\text{Discriminant}=16-32[/tex]
[tex]\text{Discriminant}=-16[/tex]
Since our discriminant is less than zero, therefore, out given trinomial will have two complex solutions and option d is the correct choice.
