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A level maths discrimination

Please help me work out:
The function g(x)=x^2+3px+(14p-3), where p is an integer, has two equal roots.
Find the value of p
Answer= p= 6
(edited 6 years ago)

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Reply 1
Original post by Musicanor
The function g(x)=x^2+3px+(14p-3), where p is an integer, has two equal roots.
Find the value of p
Answer= p= 6

Thank you
Original post by Musicanor
Please help me work out:
The function g(x)=x^2+3px+(14p-3), where p is an integer, has two equal roots.
Find the value of p
Answer= p= 6


What's the discriminant? What can you say about the discriminant if the function has two equal roots?

(Moved to maths)
Reply 3
Original post by King42415
Looks like completing the square.

(x+3/2p)^2 - (3/2p)^2 +14p - 3 = 0

Go on from there. :smile:

Okay thanks... I'll give it a go
Reply 4
b^2-4ac > 0 if has 2 real roots.
b^2-4ac = 0 if equal roots
b^2-4ac < 0 if no real solution

go from there maybe idk, I am crap at maths
Reply 5
Original post by Sonechka
What's the discriminant? What can you say about the discriminant if the function has two equal roots?

(Moved to maths)

b^2-4ac>0
Original post by Musicanor
Okay thanks... I'll give it a go


You can't find p by completing the square when you have two unknown variables in the equation. You need to use the fact that the function has two equal roots to work out p (by finding the discriminant).
Original post by Musicanor
Okay thanks... I'll give it a go


Edit: nvm, Sonechka responded before I did with almost the same reply.
Reply 8
Original post by M4cc4n4
b^2-4ac > 0 if has 2 real roots.
b^2-4ac = 0 if equal roots
b^2-4ac < 0 if no real solution

go from there maybe idk, I am crap at maths


Yep I've done that... But the answer doesn't equal 6
Original post by Musicanor
b^2-4ac>0


Yes, so what is the discriminant of this particular function? (Also, it isn't greater than 0 if it has two equal roots.)
Original post by Musicanor
Yep I've done that... But the answer doesn't equal 6


Are you using the correct values for a, b, and c? Are you able to show us your workings so far?

Be careful with what C is, it might not seem obvious at first.
Reply 11
Okay thanks.
Where have I gone wrong?
(3p)^2-4<14p-3
9p^2< 14p-3+4
9p^2< 14p + 1
p^2< 14p+1 divided by 9
Reply 12
Original post by Sonechka
Yes, so what is the discriminant of this particular function? (Also, it isn't greater than 0 if it has two equal roots.)


(3p)^2 - (4x1x[14p-3])=0
(edited 6 years ago)
Reply 13
Original post by King42415
b^2 - 4ac = 0 according the part of the question that says 2 equal roots. This means you have 9p^2 - 4*1* (14p-3) = 0

9p^2 - 56p +12 =






I can't do that in my head, so try putting that into the quadratic formula to get the values for p.
(I got the answers as 6 and 2/9). 6 is the only integer, so 6 is the answer.

Thank you sooooooooo much King
Original post by Musicanor
Okay thanks.
Where have I gone wrong?
(3p)^2-4<14p-3
9p^2< 14p-3+4
9p^2< 14p + 1
p^2< 14p+1 divided by 9


Edit: Do you understand what King had posted and why he did it that way? That's the most crucial part of all of this, even if you didn't resolve the question by yourself.
(edited 6 years ago)
9p^2-56p+12=0

(9p-2)(p-6)
Original post by King42415
b^2 - 4ac = 0 according the part of the question that says 2 equal roots. This means you have 9p^2 - 4*1* (14p-3) = 0

9p^2 - 56p +12 = 0

I can't do that in my head, so try putting that into the quadratic formula to get the values for p.
(I got the answers as 6 and 2/9). 6 is the only integer, so 6 is the answer.


Please don't post full solutions in the future; as per the maths forum posting guidelines, hints are much preferred and full solutions will be removed (unless the OP has already seen them) :smile:
Original post by King42415
Oh, sorry I didn't know this section had guidelines like that! I'll keep in it mind next time, I just got carried away, lol. I was intending to stop at the 9x^2 -56p +12 :rofl:


Maths is just too addictive, isn't it? :lol: Fair enough, now you know. Thanks for taking the time to help out here, in any case!
Not sure how I feel after reading the title
(edited 6 years ago)
Reply 19
Original post by ManLike007
Not sure how I feel after reading the title

I was relieved when I saw this thread was about the discriminant :tongue:

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