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quick discriminant question

I know that if:
b24ac=0b^2-4ac = 0 then there are no points of intersection. Is that how you'd write it though like after substituting the values, would you leave the = 0 at the end? You don't change it to something like less than or equal to or anything do you? I mean, I don't know why you would but just to be sure.

Thanks!
Just because b24ac=0 b^2 - 4ac = 0 doesn't mean that there are no solutions. You could still have a solution at b2a \frac{-b}{2a} .

There are no (real) solutions when b24ac<0 b^2 - 4ac < 0
(edited 11 years ago)
Reply 2
b24ac=0b^2-4ac=0 implies 1 point of intersection. (A repeated root)
Reply 3
Original post by claret_n_blue
Just because b24ac=0 b^2 - 4ac = 0 doesn't mean that there are no solutions. You could still have a solution at b2a \frac{-b}{2a} .

There are no (real) solutions when b24ac>0 b^2 - 4ac > 0


ooops
Original post by TenOfThem
ooops


Lol, fixed it!
Reply 5
Original post by Magenta96
I know that if:
b24ac=0b^2-4ac = 0 then there are no points of intersection. Is that how you'd write it though like after substituting the values, would you leave the = 0 at the end? You don't change it to something like less than or equal to or anything do you? I mean, I don't know why you would but just to be sure.

Thanks!


b24ac=0b^2 - 4ac = 0, then b2=4acb^2 = 4ac Therefore, ac=4,b=+or2.ac = 4, b = + or -2.

That means that if b can be multiple things, then there a two y = equations.

y=ax2+2x+cy=ax^2+2x+c
y=ax22x+cy=ax^2-2x+c

so to find the intercept equations:

0=ax2+2x+c;0=x(ax+2)+c;x(ax+2)=c0=ax^2+2x+c; 0 = x(ax+2)+c; x(ax+2) = -c
0=ax22x+c;0=x(ax2)+c;x(ax2)=c0=ax^2-2x+c; 0 = x(ax -2)+c; x(ax-2) = -c

That means x has a positive and a negative value, so there is more than 1 intercept.
(edited 11 years ago)
Reply 6
Original post by Madalaine M
b24ac=0b^2 - 4ac = 0, then b2=4acb^2 = 4ac Therefore, ac=4,b=+or2.ac = 4, b = + or -2.



Not sure what you're trying to say there, Madalaine :confused:
Reply 7
Original post by Magenta96
I know that if:
b24ac=0b^2-4ac = 0 then there are no points of intersection.

Thanks!


Woolly thinking or woolly typing.

I presume you meant to say, "there are no points of intersection with the x-axis"

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