Where does the value of $b^2 - 4ac$ come from for the discriminant??
The value under the square root sign in the quadratic formula.
Why is the discriminant useful??
It tells you how many real roots a quadratic has.
What is the formula for the discriminant??
$$ b^2 - 4ac $$
Why must a positive discriminant mean two real roots??
The square root of a positive number has two possible solutions.
Why must a zero discriminant mean one repeated root??
The square root of zero is zero; there is only one solution.
Why must a negative discriminant mean no real roots??
Because the square root of a negative number is imaginary.
How many real solutions for $b^2 - 4ac > 0$??
$$ 2 $$
How many real solutions for $b^2 - 4ac = 0$??
$$ 1 $$
How many real solutions for $b^2 - 4ac < 0$??
$$ 0 $$
How would you go about finding the values for $k$ for which $f(x) = x^2 + kx + 9$ has equal roots??
Use the fact that $b^2 - 4ac$ must equal $0$ and substitute for $k$.
Given that $y - x = k$ and $x^2 + y^2 = 4$ has one pair of solutions, what two steps could you use to show that $k = \pm2\sqrt{2}$??
- Substitute $x = k + y$ into $x^2 + y^2 = 4$ to find a quadratic in terms of $k$ and $y$.
- Use the fact the discriminant has to equal $0$ for there to be one pair of solutions.
If you have something like $4kx^2 + 2x + k + 1$, even if the discriminant is positive why does a value of $k = 0$ still mean there is only $1$ solution??
Because the $x^2$ term disappears and you get a linear equation with only one root.
Backlinks
Metadata
date: 2020-10-24 13:08
tags:
- '@?maths'
- '@?public'
title: Maths - Discriminant