Tips for Macrob

[lovelyperson]

Hello guys!
I was wondering if anyone knew how to solve this question?
Find the values of p for which the equation px²+2(p+2)x+p+7=0 has no real solution.
Thank you so much guys!

A quadratic has no real solutions when its discriminant is less than 0 (i.e negative). Discriminant = b² - 4ac, wherein a = p, b = 2(p + 2), and c = p + 7. Plug all those values in, make it < 0, then solve for p.

[Phoenix11]

Oh Ok!
Thank you so much! I figured it out.

I was wondering if anyone knew how to solve this question?
Show the equation x²+4mx+24m-44=0 has a solution for all values of m.

Also, since if a is negative and c is positive and the graph gives two solutions(in ax²+bx+c), does that mean that there are two solutions for all values of a,b,c?
Since in these questions:
a)Find the discriminant of 4mx²+4(m-1)x+m-2=0. I got the answer 16
b)Show the equation 4mx²+4(m-1)x+m-2=0 has a solution for all values of m. Since the discriminant(16) is higher than 0, there are two solutions. Now does that mean for all values of m, there are two solutions?
Thank you so much.
This is greatly appreciated.

[lovelyperson]

Oh Ok!
Thank you so much! I figured it out.

I was wondering if anyone knew how to solve this question?
Show the equation x²+4mx+24m-44=0 has a solution for all values of m.

Also, since if a is negative and c is positive and the graph gives two solutions(in ax²+bx+c), does that mean that there are two solutions for all values of a,b,c?
Since in these questions:
a)Find the discriminant of 4mx²+4(m-1)x+m-2=0. I got the answer 16
b)Show the equation 4mx²+4(m-1)x+m-2=0 has a solution for all values of m. Since the discriminant(16) is higher than 0, there are two solutions. Now does that mean for all values of m, there are two solutions?
Thank you so much.
This is greatly appreciated.

for your first question, the equation has a solution when the discriminant is greater than or equal to zero. Plug in the values and you should get something with the form am² - bm + c ≥ 0. <-- This is essentially telling us that the parabola is shaped like a smiley face. In order to show that it's positive for all values of m, you have to show that the turning point is positive (b/c if it is, the entire graph is above the x axis and therefore positive - and also all values of m). You can do this with the formula x = - b/a and using the x point you get to find the corresponding y value.

for your second question, yeah ( i think? check with someone else - i'm not entirely sure, sorry  )

[VanillaRice]

b)Show the equation 4mx²+4(m-1)x+m-2=0 has a solution for all values of m. Since the discriminant(16) is higher than 0, there are two solutions. Now does that mean for all values of m, there are two solutions?

for your second question, yeah ( i think? check with someone else - i'm not entirely sure, sorry  )

Yep, lovelyperson is right. The discriminant is 16 for all real values of m, and so this also means that there are 2 solutions for all values of m

[Phoenix11]

Thank you so much guys!
I really appreciate all your help!

Okay, so I am just posting a piece of my argumentative writing here and I was wondering if someone could give me feedback for it? I am not too sure about the arguments so it would be great if someone could confirm that my arguments are valid and make sense!
Also, when should we use will, might, may, would and should in this situation as I don't know whether we should stick to one modal verb in the whole essay or whether we can use it at different times, depending on where it makes sense. The modal verbs I am not sure about are in bold
Also, for my third paragraph, are there too many ideas and if there are should I limit it to one whole idea and expand so the main theme is more clear?
Sorry for all the questions!
Any feedback at all is greatly appreciated!
Thank you!

The minimum driving age should not be raised.

The minimum driving age exists to ensure that young, curious drivers have an experience that is worth remembering. However, raising the minimum driving age will limit the drivers' freedom. The minimum driving age should not be raised. If the driving age is raised, there would most likely be rebellious minors who may still drive without a licence anyway, causing havoc. Also, teenagers need to be able to learn from their mistakes so the driving rule should stay unaltered.

To begin with, the minimum driving age should not be raised as a teenage rebellion may arise, ultimately causing havoc. Teenagers specifically want to adhere to their own desires so if the minimum driving age is raised , they would not comply to the rules. They may create havoc in the society by persuading people to join their campaign for young drivers' rights. For example, there may be long arguments between these youngsters and their parents and other adults. This will ultimately cause unnecessary conflicts that the government will eventually have to solve so we should keep the teenagers comfortable with the current driving rule. Therefore, the minimum driving age should not be raised as unnecessary conflicts may arise within communities.

Furthermore, keeping the minimum driving age unchanged will mean that teenagers can keep making mistakes, which they can learn and benefit from. Raising the driving age will only delay the process of teenagers learning from their own mistakes when driving a car so it would advantageous if they learnt it at a younger stage when they are still accepting new things. This would eventually limit the mistakes these minors might make in the coming years. For instance, drink-driving an text-driving are global issues that affect people and individuals around them. If someone was drink-driving and nearly struck a person walking across the zebra crossing, they will learn that you shouldn't drink and drive. Since they experienced nearly killing someone, they would associate drink-driving with a bad consequence, allowing them to be more aware of their actions. Since young drivers such as 17 year olds are immature, they will have more situations to learn from their mistakes. Hence, the minimum driving age should not be raised as teenagers would be able to learn from their mistakes earlier, limiting mistakes later.

In conclusion, the minimum driving age should not be raised as teenagers might cause a rebellion, meaning conflicts may arise within the society. Also, teenagers would be able to learn from their mistakes by experiencing many situations at a younger stage.