Question

What are the possible numbers of solutions the equation ax^2+bx+c=0 can have?

Describe in detail what the graph of each possibility might look. Visual examples may count instead of a verbal description.

Answer 1

See below

Explanation:

Given equation:

• ax² + bx + c = 0

This is a polynomial of degree 2 or a quadratic equation.

This may have two, one or no solution.

See the attached for each case.

• When the equation has a root of multiplicity of 2, it touches the x-axis and has one solution (yellow graph).
• When the graph intersects the x-axis at two points, it has two solutions (blue graph).
• When no intersection with the x- axis, the graph is above or below the x-axis, then no solutions (red graph).