Download What is the discriminant?

12/12/2016
(67) Discriminant review | Solving quadratics using the quadratic formula | Quadratic equations and functions | Algebra I | Khan Academy
Discriminant review
The discriminant is the part of the quadratic formula underneath the square root symbol:
b^2-4ac. If the discriminant tells us whether there are two solutions, one solution, or no
solutions.
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Quick review of the quadratic formula
The quadratic formula says that
2
−b ± √ b − 4ac
x=
2a
for any quadratic equation like:
2
ax + bx + c = 0
What is the discriminant?
The discriminant is the part of the quadratic formula under the square root.
2
−b ± √ b − 4ac
x=
2a
The discriminant can be positive, zero, or negative, and this determines how
many solutions there are to the given quadratic equation.
A positive discriminant indicates that the quadratic has two distinct real
number solutions.
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12/12/2016
(67) Discriminant review | Solving quadratics using the quadratic formula | Quadratic equations and functions | Algebra I | Khan Academy
A discriminant of zero indicates that the quadratic has a repeated real
number solution.
A negative discriminant indicates that neither of the solutions are real
numbers.
Want to understand these rules at a deeper level? Check out this video.
Example
We're given a quadratic equation and asked how many solutions it has:
2
6x + 10x − 1 = 0
From the equation, we see:
a=6
b = 10
c = −1
Plugging these values into the discriminant, we get:
2
b − 4ac
2
=10 − 4(6)(−1)
=100 + 24
=124
This is a positive number, so the quadratic has two solutions.
This makes sense if we think about the corresponding graph.
y
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12/12/2016
(67) Discriminant review | Solving quadratics using the quadratic formula | Quadratic equations and functions | Algebra I | Khan Academy
y
4
2
−4
2
4
x
−4
Graph of y=6x^2+10x-1
Notice how it crosses the x-axis at two points. In other words, there are two
solutions that have a y -value of 0, so there must be two solutions to our
2
original equation:6x
+ 10x − 1 = 0.
Practice
PROBLEM 1
2
f (x) = 3x + 24x + 48
What is the value of the discriminant of f ?
How many distinct real number zeros does f have?
Check
Explain
Want more practice? Check out this exercise.
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(67) Discriminant review | Solving quadratics using the quadratic formula | Quadratic equations and functions | Algebra I | Khan Academy
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