Ridiculous mathematics question (1 Viewer)

[AmyLeeIsGod]

I have come across this in one of my assignments. My teacher is in Mumbai and my stand-in teacher doesn't have a clue how to solve this. I was wondering if any of you can help?

Here is the question:


For the quadratic equation: x^2 - px + 9 = 0 By x^2 i mean x squared


find p if twice the sum of the roots equals the product.


Now, by my reckoning that leaves us with an equation that has no real roots because what we are left with is:

x^2 - 4.5x + 9 = 0

and if we use the quadratic formula we end up with a negative square root.

 

[Slidey]

It has no real roots - so? Who says it has to. While as a 3u student, you do not need to know how to solve equations with complex roots, nothing says you can't do this question. You are certainly meant to be able to recognise when an equation has complex roots, as you did.

Essentially, you are correct. The equation's roots, though you don't need to know them, are:

x = (4.5 +/- sqrt(81/4 - 36))/2 = (4.5 +/- sqrt(15/4)i)/2
x = (4.5+/-sqrt(15)i)/2

Now, add both of those roots together and double the result, and you'll find you get 9.

 

[airie]

Heh, what assignment is this? From a 3u prelim course? You could either write the complex roots, or just write "no real solutions" if you're feeling lazy

The equation's roots, though you don't need to know them, are:

x = (4.5 +/- sqrt(81/4 - 36))/2 = (4.5 +/- sqrt(15/4)i)/2
x = (4.5+/-sqrt(15)i)/2

Now, add both of those roots together and double the result, and you'll find you get 9.

Uhh, you sure? I got x = (4.5 +/- 1.5*sqrt7*i)/2. o.0

 

[shimmerz_777]

let the roots = a and b

a + b = p

ab = -9

now 2(a + b)= ab
so 2(a + b) = 2p = -9

p=-9/2

easy, dont know how u did it any other way

 

[Riviet]

Just a correction, ab should equal 9, not -9 because product of roots = c/a = 9/1.

 

[Shady01]

there no longer Ridiculous is it

 

[shimmerz_777]

ur right my bad. darn those silly mistakes!!!!!!!!!!!!!!