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
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
1 answer