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