I don't understand why the discriminant is used here

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val7322
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#1
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#1
I don't understand the answer to the question
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Muttley79
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(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
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val7322
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(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?
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leenthedoormat
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The thing is I don’t understand either. We’re the same bro.
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The A.G
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(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
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Muttley79
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(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.
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val7322
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#7
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(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
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The A.G
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(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
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B_9710
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(Original post by val7322)
but what does a<-7/16 mean
Consider an easier example if you are confused. Consider the curve  y=x^2 + a and the line  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=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.
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val7322
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(Original post by B_9710)
Consider an easier example if you are confused. Consider the curve  y=x^2 + a and the line  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=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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