xxMsJojoxx
Junior Member
- Joined
- Oct 6, 2020
- Messages
- 54
Thanks for the hint. I now tried using the quadratic formula, to find the vertex of the 2 equations.Before factoring why not divide by 5?? Can we see your factoring attempts?
Is factoring the only way you know how to solve a quadratic equation?
Have you learned about completing the square method or using the quadratic formula?
Thank you. That was the answer given in my textbook. This is a review question for a Math Course in College.If you rely on memorizing formulas, be sure to remember what each formula is for. What you chose is not the quadratic formula. Let’s start with the formula for profit:
Profit = revenue - cost =
[MATH](- 2x^2 + 100x + 50) - (3x^2 - 10x + 200) = - 5x^2 + 110x - 150.[/MATH]
Now stop to think a moment. If x has a large absolute value, then profit will be negative because - 5x2 will be hugely negative. Thus, profit will be positive only for those values of x that lie between the x-intercepts (if there are any).
Now how do we find those x-intercepts. We set our equation to zero and use the quadratic formula.
[MATH]-5x^2 + 110x - 150 = 0 \implies x^2 - 22x + 30 = 0 \implies[/MATH]
[MATH]x = \dfrac{22 \pm \sqrt{22^2 - 4(1)(30)}}{2 * 1} = \dfrac{22 \pm \sqrt{484 - 120}}{2} = 11 \pm \sqrt{91}.[/MATH]
Now when you evaluate that you don’t get 2 or 20 as a result. So why are 2 and 20 the correct answers?
Glad to have helped, but you did not answer my final question?Thank you. That was the answer given in my textbook. This is a review question for a Math Course in College.
I agree that it is the correct answer. But if you find the x-intercepts of your profit function, they are not 2 and 20. So WHY are 2 and 20 the correct answers?2 to 20 is the answer given in my textbook, for this question.
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I don't know . I tried plugging in x in the original equation as well.I agree that it is the correct answer. But if you find the x-intercepts of your profit function, they are not 2 and 20. So WHY are 2 and 20 the correct answers?