Question
which of the polynomials has solutions that are not real numbers
x^2 - 6x + 3
x^2 + 4x + 3
-x^2 - 9x - 10
x^2 + 2x + 3
x^2 - 6x + 3
x^2 + 4x + 3
-x^2 - 9x - 10
x^2 + 2x + 3
Answers
Answer
explain why
Answered by
GPT 3.5
-x^2 - 9x - 10
Answered by
GPT 3.5
A polynomial has solutions that are not real numbers when its discriminant is negative. The discriminant of a quadratic polynomial of the form ax^2 + bx + c is given by Δ = b^2 - 4ac.
For the polynomial -x^2 - 9x - 10, we can identify a = -1, b = -9, and c = -10.
Now, let's calculate the discriminant:
Δ = (-9)^2 - 4*(-1)*(-10)
Δ = 81 - 40
Δ = 41
Since the discriminant Δ = 41 is positive, the quadratic polynomial -x^2 - 9x - 10 has real solutions.
Therefore, the polynomial that has solutions that are not real numbers is x^2 + 2x + 3 because when we calculate its discriminant, the result is Δ = 4 - 4*1*3 = 4 - 12 = -8, which is a negative value.
For the polynomial -x^2 - 9x - 10, we can identify a = -1, b = -9, and c = -10.
Now, let's calculate the discriminant:
Δ = (-9)^2 - 4*(-1)*(-10)
Δ = 81 - 40
Δ = 41
Since the discriminant Δ = 41 is positive, the quadratic polynomial -x^2 - 9x - 10 has real solutions.
Therefore, the polynomial that has solutions that are not real numbers is x^2 + 2x + 3 because when we calculate its discriminant, the result is Δ = 4 - 4*1*3 = 4 - 12 = -8, which is a negative value.
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