SOLUTION: y= 3 y= ax^2 + b In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solution

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Question 1046378: y= 3
y= ax^2 + b
In the system of equations above, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions?
A) a= -2, b= 2
B) a= -2, b= 4
C) a= 2, b= 4
D) a= 4, b= 3
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Equating the two expressions for Y,
ax%5E2%2Bb=3

Putting into general form,
ax%5E2%2Bb-3=0


Use the DISCRIMINANT.
You want two real solutions.
Understand clearly that b here is not the same meaning as b in "ax^2+bx+c".


YOUR discriminant is 0%5E2-4%2Aa%2A%28b-3%29=highlight_green%28-4a%28b-3%29%3E0%29.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


This requires evaluation of the discriminant, but since the coefficient is used in a non-standard way in the statement of the problem, I'm going to use:



as the general quadratic equation and then the discriminant is



Multiply your first equation by -1:



Then add the two equations:



Now the coefficients of your quadratic are , , and

Substituting into the discriminant:



In order for there to be two distinct solutions, must be strictly greater than zero. Try each pair of values for and until you find one that fits. Check them all; there might be more than one.

John

My calculator said it, I believe it, that settles it