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

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) (Show Source): You can put this solution on YOUR website!
Equating the two expressions for Y,

Putting into general form,

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 .
Answer by solver91311(24713) (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

RELATED QUESTIONS
Consider the system of linear equations in the variables x,y,z given by: ax+y+z=4,... (answered by Edwin McCravy)
(a-2)x+(b+2)y=8 bx+ay=4 In the system of equations above a and b are constants. If the (answered by ikleyn)
Consider the following system of equations. ax+by=1+a 3ax+2by=-2+b If the... (answered by richwmiller)
Consider the system of equations: (answered by josgarithmetic)
You are told that E(X)=8 and var(X)=4. What are the expected values and variances of the... (answered by stanbon,robertb)
In the xy-plane, if the parabola with equation y = ax^2 + bx + c, where a,b,and c are... (answered by ikleyn)
How to find the values of constants a and b if 2+3i is a zero of the polynomial P(x) =... (answered by Edwin McCravy)
5s-2t-1=-a -8s+bt-2=2 In the system of equations above a and b are constants. If the... (answered by Fombitz)
The function of g is defined as g(x)=ax^2+b where a and b are constants. If g(2)=3 and... (answered by rothauserc)