Question

In math class, Julia and Ricardo are analyzing the
function f(x) = -x^2 + 4x - 14, Julia thinks there
are no real zeros in this function, and Ricardo says there is one real zero. Who is right?
(1 point)

ricardo is right because the discriminant of this function is zero

julia is right because the function has two real zeros

ricardo is right because the function has one real zero

julia is right because the function has no real zeros
Answer
are you sure
Answer
what's your final answer
Answer
WHAT IS THE CORRECT ANSWER
Answered by GPT 3.5
ricardo is right because the function has one real zero.
Answered by GPT 3.5
I apologize for the confusion. Let's calculate the real zeros of the function.

To find the real zeros of the function f(x) = -x^2 + 4x - 14, we need to find the values of x for which f(x) = 0.

Setting f(x) = 0, we get:
-x^2 + 4x - 14 = 0

To find the real zeros, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -1, b = 4, and c = -14.

Plugging these values into the quadratic formula, we get:
x = (-(4) ± √((4)^2 - 4(-1)(-14))) / 2(-1)
x = (-4 ± √(16 - 56)) / -2
x = (-4 ± √(-40)) / -2
x = (-4 ± 2√10i) / -2
x = -2 ± √10i

Since the square root of a negative number results in a complex number, there are no real zeros for this function.

Therefore, Julia is right because the function has no real zeros. Thank you for pointing out that mistake.
Answered by GPT 3.5
Julia is right because the function has no real zeros.
Answered by GPT 3.5
I apologize for the oversight in my responses. The correct answer to the question "Julia and Ricardo are analyzing the function f(x) = -x^2 + 4x - 14. Julia thinks there are no real zeros in this function, and Ricardo says there is one real zero. Who is right?" is:

Julia is right because the function has no real zeros.