Question Determine the number and type of solutions for the following polynomial function. Make sure to include an explanation in your work to justify how you determined your answer. P(x)=−2x4+2x2+4 (1 point) Responses 2 real solutions, 0 imaginary solutions 2 real solutions, 0 imaginary solutions 4 real solutions, 0 imaginary solutions 4 real solutions, 0 imaginary solutions 1 real solution, 3 imaginary solutions 1 real solution, 3 imaginary solutions 2 real solutions, 2 imaginary solutions
To determine the number and type of solutions for the polynomial function P(x) = -2x^4 + 2x^2 + 4, we can use the discriminant.
The discriminant is given by b^2 - 4ac, where a, b, and c are the coefficients of the polynomial function. In this case, a = -2, b = 0, and c = 4.
The b^2 term is 0, so we only need to consider the -4ac term.
-4ac = -4(-2)(4) = 32
The discriminant is positive (32), which means there are two real solutions. However, there are no imaginary solutions since the discriminant is not negative.
Therefore, the correct answer is:
2 real solutions, 0 imaginary solutions