Question

How many solutions are possible for a system of equations containing exactly one linear and one quadratic equation? (Select all that apply). 0 1 2 3 4

Answer 1

Remember that a quadratic equation is a parabola. The equation is of the type y = Ax^2 + Bx + C


A linear equation is a straight line. The equation is of the type y = MX + N


The soluction of that system is Ax^2 + Bx + C = MX + N

=> Ax^2 + (B-M)x + (C-N) = 0


That is a quadratic equation.


A quadratic equation may have 0, 1 or 2 real solutions. Those are all the possibilitis.


So you must select 0, 1 and 2.


You can also get to that conclusion if you draw a parabola and figure out now many point of it you can intersect with a straight line.


You will realize that depending of the straight line position it can intersect the parabola in none point, or one point or two points.