Reading the Sign

Part of the Quadratics & Complex Numbers section of Coddy's Algebra 2 journey. Lesson 35 of 51.

You do not need to solve a quadratic to know what its solutions look like. Compute the discriminant and read its sign. Take 2x^2 + 3x + 4 = 0: the discriminant is 3^2 - 4 × 2 × 4, which is 9 - 32, or -23. Negative, so the equation has two complex solutions and no real ones.

For this question only the sign matters, not the size. -23 and -1 both mean complex solutions; 16 and 3 both mean two real ones. The size matters once you solve: a perfect square like 16 gives answers without a root sign, while 3 leaves the square root of 3 in them.

The sign also shows on the graph. The real solutions of ax^2 + bx + c = 0 are the x values where y = ax^2 + bx + c crosses the x-axis. A positive discriminant means two crossings, zero means the vertex just touches the axis, and a negative one means the parabola misses the axis entirely.

Challenge

Find the discriminant of 3x^2 + 6x + 5 = 0. The board holds b^2 - 4ac with a, b and c put in: type each line until one number is left. Before you press Check, read its sign: what kind of solutions does the equation have?

Try it yourself

6^2 - 4 * 3 * 5

Simplify the expression