Card 1 of 8
MediumStudy card 1
Prompt
When can you use the zero-product property?
Answer
After one side equals zero and the other side is written as a product; set each factor equal to zero.
MathAdvanced Math
Flashcards
Nonlinear Equations Flashcards
Recall nonlinear solution methods, root checks, and extraneous-solution traps.
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Card 1 of 8. Answer hidden.
Card 2 of 8
MediumStudy card 2
Prompt
What is the quadratic formula?
Answer
For ax² + bx + c = 0, substitute a, b, and c carefully—including their signs.
Quadratic formula
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
Card 3 of 8
MediumStudy card 3
Prompt
What does the discriminant tell you?
Answer
Positive: two real roots. Zero: one repeated real root. Negative: no real roots.
Discriminant
\[b^2-4ac\]
Card 4 of 8
MediumStudy card 4
Prompt
Why include ± after taking an even root?
Answer
Both the positive and negative values can square to the same number.
Card 5 of 8
MediumStudy card 5
Prompt
What is an extraneous solution?
Answer
A value introduced by an algebraic operation that fails in the original equation.
Card 6 of 8
MediumStudy card 6
Prompt
Why must radical-equation answers be checked?
Answer
Squaring both sides can create extraneous solutions.
Card 7 of 8
HardStudy card 7
Prompt
What restrictions should you identify before solving?
Answer
Denominators cannot be zero, and even-root radicands must be nonnegative in real-number problems.
Card 8 of 8
MediumStudy card 8
Prompt
What is a useful first move for many polynomial equations?
Answer
Move all terms to one side, factor if possible, then apply the zero-product property.
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