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 calculated using the equation b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, the polynomial P(x) is a quadratic function (-2x^4 + 2x^2) with no linear term (b = 0), and a constant term of 4 (c = 4). Therefore, the discriminant can be calculated as follows:
Discriminant = b^2 - 4ac
= 0^2 - 4(-2)(4)
= 0 + 32
= 32
Since the discriminant is positive (32 > 0), the quadratic equation has two real solutions.
Therefore, the correct answer is:
2 real solutions, 0 imaginary solutions.
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
1 real solution, 3 imaginary solutions
1 real solution, 3 imaginary solutions
2 real solutions, 2 imaginary solutions
2 real solutions, 2 imaginary solutions
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 answer