Below are several statements about the quadratic equation

$$ax^2 + bx + c = 0,$$

where $a$, $b$ and $c$ are allowed to be any real numbers except that $a$ is not $0$.

For each statement, decide whether it is ALWAYS true, SOMETIMES true, or NEVER true.

Do you have (or can you come up with) any favourite examples of quadratics with different numbers of real roots? Having some examples to test is a good way to tackle a question like this.

How can we use the coefficients of a quadratic equation to tell us about its number of real roots? How does the quadratic formula come into this?

**This is an Underground Mathematics resource **

$$ax^2 + bx + c = 0,$$

where $a$, $b$ and $c$ are allowed to be any real numbers except that $a$ is not $0$.

For each statement, decide whether it is ALWAYS true, SOMETIMES true, or NEVER true.

Do you have (or can you come up with) any favourite examples of quadratics with different numbers of real roots? Having some examples to test is a good way to tackle a question like this.

How can we use the coefficients of a quadratic equation to tell us about its number of real roots? How does the quadratic formula come into this?