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Quadratic Equation help

I've been asked to find the distance of PQ in terms of 'p' and form an equation using co-ordinates P(p,3) and Q(-1,2p) & PQ=5, and ultimately find out the value(s) of p.

So i've gotten as far as this equation
5p^2-10p-15=0
but don't know my next step. I thought maybe i factorise it but i'm struggling here.

If someone could show the working/explain how they got from my equation to deducing the value of 'p' i'd be grateful. Thank you.
(edited 8 years ago)
Original post by kneestochest
I've been asked to find the distance of PQ in terms of 'p' and form an equation using co-ordinates P(p,3) and Q(-1,2p) & PQ=5, and ultimately find out the value(s) of p.

So i've gotten as far as this equation
5p^2-10p-15=0
but don't know my next step. I thought maybe i factorise it but i'm struggling here.

If someone could show the working/explain how they got from my equation to deducing the value of 'p' i'd be grateful. Thank you.


Taking out a factor from your equation may help you to see how to factorise it.
Reply 2
Avatar for B_9710
B_9710
18
You could divide the equation by 5 on both sides giving p^2 -2p -3 = 0
Now solve for p
If you're unsure about solving/factorising quadratics when the coefficient of x^2 is not 1 then have a look on some videos about how to do it - as it will come up everywhere in A-level maths
Original post by B_9710
You could divide the equation by 5 on both sides giving p^2 -2p -3 = 0
Now solve for p
If you're unsure about solving/factorising quadratics when the coefficient of x^2 is not 1 then have a look on some videos about how to do it - as it will come up everywhere in A-level maths


Then it is (p+1) (p-3)
How did you get 5p^2-10p-15?
Reply 5
Avatar for kneestochest
kneestochest
OP
I'm resitting after being out of the game for 7 years :biggrin: I'm a bit rusty hehe. Thanks for the quick replies.
Reply 6
Avatar for kneestochest
kneestochest
OP
Original post by richpanda
How did you get 5p^2-10p-15?

I used the formula for calculating the distance between 2 points.. i'm pretty sure that's right? :s-smilie:
Reply 7
Avatar for HenryHS
HenryHS
2
For quadratics, the general formula is: x=(-b±sqrt(b2-4ac))/(2a) for ax2+bx+c

(sorry it looks slightly strange, not sure how to code ^^)

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