Question

Find the set of values of p such that px^2+2x+4p < 0 for all x.

Answer 1

if this is true for all x then its D <0

Answer 2

Sorry, if i could get some working. I would appreciate it.

Answer 3

does it make sense?

Answer 4

y= px^2+2x+4p and y<0 for all x

Answer 5

Sorry, i have no idea where you are coming from?

Answer 6

ok...u have written some quadratic expression...px^2+2x+4p...right?

Answer 7

Its under the chapter of quadratics. And yes i have written that.

Answer 8

u know that curve of a quadratic is a parabola?

Answer 9

Assume all medium levels of knowledge.

Answer 10

ok....

Answer 11

Im from australia and here i do the highest level of maths for my respective grade, 11.

Answer 12

ok

Answer 13

how many roots a quadratic equation has?

Answer 14

ok....let's draw the curve y = x^2 +3x+4

Answer 15

are you comfortable with this?

Answer 16

Yes, I can understand that much. I'm the one in the class who always wants to know why. Why do we remove the p for now? Sorry if its a simple question, i just want to be able to repeat this to someone else if they ask.

Answer 17

i am not saying that it's a simple question...and simplicity depends on whether one knows or not? even if I had not known to solve this then it wud have been a difficult question for me

Answer 18

let's draw the curve y = x^2 +3x+4

Answer 19

So we remove the pronumeral which they wish us to find?

Answer 20

we draw the curve y = x^2 +3x+4

Answer 21

Do you mean y=x^2+2x+4?

Answer 22

still there?

Answer 23

Yes. Im here and willing to listen.

Answer 24

isolate the terms with 'p'

Answer 25

factor out p

Answer 26

divide both sides by the factor of p (it will be negative so the <> sign must reverse)

Answer 27

p< -2x/(x^2+4)

Answer 28

Im with you.

Answer 29

check the range of -2x/(x^2+4) to find allowed values for p

Answer 30

Range as in Domain and Range?

Answer 31

yes

Answer 32

In terms of x or p?

Answer 33

-2x/(x^2+4) has an absolute min

Answer 34

if you're not doing calc. yet... hmm.

Answer 35

are you?

Answer 36

No I am doing calc.

Answer 37

ah easy then

Answer 38

find the min of -2x/(x^2+4)

Answer 39

p is any value less than that min

Answer 40

Its in a quadratic section though, so I would prefer not to use calc.

Answer 41

hmm yeah I think you can use the vertex form that someone mentioned briefly before deleting the comment to do it a different way...