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
7 answers
ricardo is right because the function has one real zero.
are you sure
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.
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.
what's your final answer
Julia is right because the function has no real zeros.
WHAT IS THE CORRECT ANSWER
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.
Julia is right because the function has no real zeros.