i'm not sure i understand what statements (1) and (2) are supposed to say here; please post clear and unambiguous versions of statements (1) and (2).
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in any case, here's a start:
since you're looking for an intersection point, you know that the y coordinates have to be the same. therefore, ax - b must equal x^2 + b, which means that ax - x^2 = 2b, or, x(a - x) = 2b.
can't get any farther without the statements.
Line Intersection
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mayank_gupta123
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Interesting question!
If there is at all an intersection, it would be a single point (obvious)
In that case
=> aX - b = X2 + b
=> X2 – aX + 2b = 0
For a real solution of X,
i.è. B2 – 4AC > 0
i.e. (-a)2 – 4 * 2b >0
i.e. b < a2/8
Irrespective of any sign of a, if b is less than zero, that would do the needful, therefore B should be the right answer.
Regards,
Mayank
If there is at all an intersection, it would be a single point (obvious)
In that case
=> aX - b = X2 + b
=> X2 – aX + 2b = 0
For a real solution of X,
i.è. B2 – 4AC > 0
i.e. (-a)2 – 4 * 2b >0
i.e. b < a2/8
Irrespective of any sign of a, if b is less than zero, that would do the needful, therefore B should be the right answer.
Regards,
Mayank
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cubicle_bound_misfit
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mayank,
let go parabola but whenever a single degree equation cuts an n degree equation there will be a n point cut.
let go parabola but whenever a single degree equation cuts an n degree equation there will be a n point cut.
Cubicle Bound Misfit
since I cannot see the options, I don't know the final response but here is a way to solve it:
x^2 + B = Ax - B
<=> x^2 - Ax + 2B = 0 <=>
<=> x=[A +- sqrt(A^2 - 8B)]/2
therefore we have to analyse de root:
if A^2 - 8B < 0 - No intersection
if A^2 - 8B = 0 - One intersection
if A^2 - 8B > 0 - two intersections
To anwser the question we need to know if there is at least one inters, i.e., A^2 - 8B >=0,
Thus,
[A >= sqrt(8B) or A < -sqrt(8B) ] and b>0
Now we can only anwser depending on the info given..
x^2 + B = Ax - B
<=> x^2 - Ax + 2B = 0 <=>
<=> x=[A +- sqrt(A^2 - 8B)]/2
therefore we have to analyse de root:
if A^2 - 8B < 0 - No intersection
if A^2 - 8B = 0 - One intersection
if A^2 - 8B > 0 - two intersections
To anwser the question we need to know if there is at least one inters, i.e., A^2 - 8B >=0,
Thus,
[A >= sqrt(8B) or A < -sqrt(8B) ] and b>0
Now we can only anwser depending on the info given..
