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I don't understand why the discriminant is used here

I don't understand the answer to the question
(edited 2 years ago)
Original post by val7322
I don't understand the answer to the question


For (b) the discriminant tels us information about how many real roots the quadratic has.

discrimant > 0 two real roots; = 0 two equal roots: < 0 no real roots
Reply 2
Original post by Muttley79
For (b) the discriminant tels us information about how many real roots the quadratic has.

discrimant > 0 two real roots; = 0 two equal roots: < 0 no real roots

but its asking for the range of values for a not for the number of roots?
The thing is I don’t understand either. We’re the same bro.
Original post by val7322
but its asking for the range of values for a not for the number of roots?

You sub the equations together and rearrange which gives you a general equation where a varies.For the graphs to have two points of intersection the general equation found needs to have two roots,thus you use discriminant
Original post by val7322
but its asking for the range of values for a not for the number of roots?

I thought you wrre asking about part (b)

For (c) put the two equations equal - reaarange into a quadratic then you know the dicriminant must be >0

Do that and post what you get - then we can look at solving the inequality.
(edited 2 years ago)
Reply 6
Original post by The A.G
You sub the equations together and rearrange which gives you a general equation where a varies.For the graphs to have two points of intersection the general equation found needs to have two roots,thus you use discriminant

but what does a<-7/16 mean
Original post by val7322
but what does a<-7/16 mean

It’s the condition that when a is less than -7/16 the graphs will have two points of intersection
Reply 8
Original post by val7322
but what does a<-7/16 mean

Consider an easier example if you are confused. Consider the curve y=x2+a y=x^2 + a and the line y=0 y=0 which is of course just the x-axis. You should be able to see that if a>0 then the curve lies completely above the x-axis so there are no points where the graphs intersect. If a=0 then there is a single (repeated) root. If a<0 then there are two distinct points of intersection.
So if someone told you that the curve y=x2+a y=x^2 +a crosses the x-axis at two distinct points then you’d have to have a<0.
This is the same as your example, it’s just a bit more complicated.
Reply 9
Original post by B_9710
Consider an easier example if you are confused. Consider the curve y=x2+a y=x^2 + a and the line y=0 y=0 which is of course just the x-axis. You should be able to see that if a>0 then the curve lies completely above the x-axis so there are no points where the graphs intersect. If a=0 then there is a single (repeated) root. If a<0 then there are two distinct points of intersection.
So if someone told you that the curve y=x2+a y=x^2 +a crosses the x-axis at two distinct points then you’d have to have a<0.
This is the same as your example, it’s just a bit more complicated.

thank you so much, i understand now

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