Equation in quadratic form
from class: College Algebra Definition An equation is in quadratic form if it can be written as $a(x^2 + bx + c) = 0$ where $a, b,$ and $c$ are constants. It often involves substituting a variable to simplify into a standard quadratic equation.
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Predict what's on your test 5 Must Know Facts For Your Next Test Quadratic form equations can be solved by substitution to transform them into standard quadratics. The general format is $A(u)^2 + B(u) + C = 0$ where $u$ is an expression involving the original variable. Common methods for solving include factoring, completing the square, and using the quadratic formula. Recognizing the structure of a quadratic form is crucial for correctly applying solution methods. Solutions may sometimes involve finding the roots of the substituted variable first before back-substituting. Review Questions What substitution would you use to solve $x^4 - 5x^2 + 6 = 0$? How do you recognize an equation that can be put into quadratic form? What methods can be used to solve equations once they are in quadratic form? "Equation in quadratic form" also found in:
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