SAT - Math - Quadratic Equations
For which of the following values of a and b does the system of equations have exactly two real solutions? y = 3 y = ax^2 + b
For which of the following values of a and b does the system of equations have exactly two real solutions?
y = 3
y = ax2 b
A) a= -2, b= 2
B) a= -2, b= 4
C) a= 2, b= 4
D) a= 4, b= 3
Please revise this question. One equation fixes the value of y to be 3. If we follow this, second equation becomes 3=ax^2.b now, this is a quad. eqn. which will always have two real solutions. If the question actually says y=ax^2+b, we have, 3=ax^2+b ax^2+b-3+0 using Shree Dharacharya formula (otherwise known as the quadratic formula), x=[-b+-(b^2-4ac)^1/2]/2a x=[-b+-(b^2+12a)^1/2]/2a for two real values make discriminant , b^2-4ac,greater than zero b^2+12a>0 Easiest way out is to check with the given options, We get, (C) and (D) are both correct.