Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Equations
A polynomial equation is an equation that involves a polynomial expression, which is a sum of terms consisting of variables raised to non-negative integer powers. In this case, the equation 9x^4 = 25x^2 - 16 is a polynomial equation of degree 4, as the highest power of x is 4. Understanding polynomial equations is crucial for solving them, as it involves finding the values of x that satisfy the equation.
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Substitution Method
The substitution method is a technique used to simplify equations by replacing a variable or expression with another variable. In this problem, we can let y = x^2, transforming the original equation into a quadratic form: 9y^2 - 25y + 16 = 0. This method makes it easier to solve higher-degree polynomial equations by reducing them to a more manageable form.
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Quadratic Formula
The quadratic formula is a solution method for quadratic equations of the form ax^2 + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a). Once the original equation is transformed into a quadratic form through substitution, this formula can be applied to find the roots of the equation. Understanding how to use the quadratic formula is essential for solving the resulting quadratic equation effectively.
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