Final answer:
To solve an equation using the known root 2, we substitute this value into the equation to reduce the number of unknowns, which simplifies solving the system of equations. For quadratic equations, knowing one root helps in finding the other root using the Quadratic Formula.
Step-by-step explanation:
To solve an equation when given 2 as a root of another equation, we integrate this information into our problem-solving strategy. If 2 is a root, it means that when we substitute x with 2 in the polynomial equation, the result is zero. Therefore, one of the factors of the polynomial is likely of the form (x - 2).
Let's consider the generic form of a quadratic: ax^2 + bx + c = 0. If 2 is a root, then we have a(2)^2 + b(2) + c = 0. We can use this equation to find one of the coefficients if two others are known, or use it to reduce the number of unknowns in a system of equations.
For instance, if we have a system where the second equation is dependent on one variable, substituting 2 into this equation will help eliminate one unknown, leaving us with a simpler equation to solve. For a given quadratic equation, there are two solutions provided by the Quadratic Formula: x = [-b ± sqrt(b^2-4ac)]/(2a). Therefore, knowing one root can significantly simplify our computations.