ChatGPT Got an F
(1) My first question asked for a solution to
y'(t) = k y(t) (b - y(t))
Right away Chat noticed that this was calculus and would involve exponential growth. Then it gave me links to references with examples of exponential growth and differential equations.
But the response was nothing like a solution, e.g., in TeX:
y(t) = { y(0) b e^{bkt} \over y(0) \big ( e^{bkt} - 1 \big ) + b }
So, Chat can respond with content about differential equations but can't actually solve an exercise in first calculus.
(2) I gave Chat the question:
Given triangle ABC, construct D on side AB and E on side BC so that the lengths AD = DE = EC.
Chat had no answer, not even a hint or clue, how to do that.
But it did present some materials on triangles, all either irrelevant or not better than trivially relevant.
My Response: For some queries Chat may be a little better than Bing or Google.
2 comments
[ 3.0 ms ] story [ 17.6 ms ] threadQ. What are the roots of the equation x^2 - x - 6 = 0
A. To find the roots of the equation x^2 - x - 6 = 0, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, a = 1, b = -1, and c = -6. Substituting these values into the formula, we get:
x = (-(-1) ± sqrt((-1)^2 - 4(1)(-6))) / 2(1) x = (1 ± sqrt(1 + 24)) / 2 x = (1 ± sqrt(25)) / 2
Simplifying, we get:
x1 = (1 + 5) / 2 = 3 x2 = (1 - 5) / 2 = -2
Therefore, the roots of the equation x^2 - x - 6 = 0 are x = 3 and x = -2.
Q. Could you solve it more easily by factoring the polynomial?
A. Yes, you can also solve the equation x^2 - x - 6 = 0 by factoring the polynomial.
To do this, we need to find two numbers whose product is -6 and whose sum is -1, which are -3 and 2.
Then, we can rewrite the polynomial as:
x^2 - x - 6 = (x - 3)(x + 2) = 0
Using the zero product property, we know that either (x - 3) = 0 or (x + 2) = 0.
Therefore, the roots of the equation are x = 3 and x = -2, which are the same values we obtained using the quadratic formula.
So, the factored form of the polynomial is (x - 3)(x + 2) = 0, and its roots are x = 3 and x = -2.