Hey Kelting
In your solution here, you find only one solution for x. In parabolas like these however, there are two x intercepts.
How do you find the second following your method?
Hey Corey,
If you look carefully, there are two solutions which is denoted by the "±" symbol.
Hey guys. Im looking at how the quadratic formula is made through the process of conpleting the square on the general quadratic equation.
I dont understand the algebra at the start though. It looks to me like they are forgetting to put a square sign on the a?
Am I the one making the mistake?
Many thanks,
Corey
Yep this is a mistake on the textbook. Great job exploring the formulas and not taking them for granted
. This "inquiry based" mindset will set you up well for your future studies.
Hi! This is a question from a past VCE examination, Exam 2. The question is as follows:
I attempted to solve this by solving the simultaneous equation:
However, my CAS is unable to give me an exact answer. The output was k = 0.367879 which corresponds to the answer 1/e but I remember seeing this as an extended response question too somewhere else and I would have lost marks in that case because my CAS wasn't able to determine the exact answer.
Does anyone here have any suggestions on what to input into the CAS to get an exact answer?
A screenshot of my CAS input is attached.
Hey Dogwhip,
Sometimes the CAS cannot solve for exact solutions unfortunately. However, if an exact solution is required, it is always possible to solve it by hand.
Let Eq1 be e
kx = x, Eq2 be k×e
kx = 1.
By subbing Eq1 into Eq2, we have k×x = 1, x = 1/k
Now we can sub this back into Eq1: e
k×1/k = x, hence x = e, k = 1/e
Sometimes when trigonometric or exponential equations are involved, the CAS cannot give u an exact answer, so it is worth learning how to do these by hand.
Hope this helps!
James