Question
In math class, Jane and Ricky are analyzing the function f(x) -x^2 + 4x - 14. Jane thinks there are no real zeros in this function, and Ricky says there is one real zero. Who is right?
a) Jane is right because the function has two real zeros
b) Jane is right because the function has no real zeros
c) Ricky is right because the function has one real zero
d) Ricky is right because the discriminant of this function is zero.
a) Jane is right because the function has two real zeros
b) Jane is right because the function has no real zeros
c) Ricky is right because the function has one real zero
d) Ricky is right because the discriminant of this function is zero.
Answers
Answer
Did you calculate the discriminant? Are you sure it has ONE REAL ZERO and after you calculate the discriminant it will show it has NO REAL ZEROS
Answered by
GPT 3.5
Ricky is right because the function has one real zero.
To find the zeros of the function, we need to find the values of x for which f(x) = 0. We can do this by setting -x^2 + 4x - 14 = 0 and solving for x.
The discriminant of a quadratic function in the form ax^2 + bx + c is given by b^2 - 4ac. If the discriminant is greater than zero, the function has two real zeros. If the discriminant is equal to zero, the function has one real zero. If the discriminant is less than zero, the function has no real zeros.
In this case, the discriminant of -x^2 + 4x - 14 is equal to 4^2 - 4(-1)(-14) = 16 - 56 = -40, which is less than zero. Therefore, the function has one real zero.
To find the zeros of the function, we need to find the values of x for which f(x) = 0. We can do this by setting -x^2 + 4x - 14 = 0 and solving for x.
The discriminant of a quadratic function in the form ax^2 + bx + c is given by b^2 - 4ac. If the discriminant is greater than zero, the function has two real zeros. If the discriminant is equal to zero, the function has one real zero. If the discriminant is less than zero, the function has no real zeros.
In this case, the discriminant of -x^2 + 4x - 14 is equal to 4^2 - 4(-1)(-14) = 16 - 56 = -40, which is less than zero. Therefore, the function has one real zero.
Answered by
GPT 3.5
Apologies for the error in my previous response. Let's calculate the discriminant of the function -x^2 + 4x - 14 correctly.
The quadratic function is in the form -x^2 + 4x - 14, so a = -1, b = 4, c = -14.
The discriminant is calculated as b^2 - 4ac:
Discriminant = 4^2 - 4*(-1)*(-14)
Discriminant = 16 - 56
Discriminant = -40
Since the discriminant is negative (-40), the function has no real zeros.
Therefore, Jane was correct in her assertion that there are no real zeros in the function. The correct answer is:
b) Jane is right because the function has no real zeros.
The quadratic function is in the form -x^2 + 4x - 14, so a = -1, b = 4, c = -14.
The discriminant is calculated as b^2 - 4ac:
Discriminant = 4^2 - 4*(-1)*(-14)
Discriminant = 16 - 56
Discriminant = -40
Since the discriminant is negative (-40), the function has no real zeros.
Therefore, Jane was correct in her assertion that there are no real zeros in the function. The correct answer is:
b) Jane is right because the function has no real zeros.