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\( B \quad F ( x ) = x ^ { 2 } + 5 x + 6 \)

Ask by Garza Phillips. in Argentina
Feb 24,2025

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La función es F(x) = x² + 5x + 6, que se puede factorizar como (x + 2)(x + 3). Las raíces son x = -2 y x = -3.

Solución

La función definida es F(x) = x² + 5x + 6. Esta función cuadrática se puede factorizar. Para ello, buscamos dos números que al multiplicarse den 6 y al sumarse den 5. Esos números son 2 y 3. Por lo tanto, la factorización es:   F(x) = (x + 2)(x + 3) Esto también nos indica que las raíces de la función, es decir, los valores de x que hacen F(x) = 0, son x = -2 y x = -3.

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Mind Expander

Did you know that the function \( F(x) = x^2 + 5x + 6 \) is a classic example of a quadratic function? Quadratics like this one graph as parabolas and can be easily analyzed to find their maximum or minimum points, roots, and intercepts. This specific function can be factored into \( (x + 2)(x + 3) \), showing its roots at \( x = -2 \) and \( x = -3 \)! In real life, quadratic functions pop up in various fields such as physics, finance, and engineering. For example, when launching an object, the path it takes can be described by a quadratic equation. Understanding how to manipulate these functions can help solve problems, such as predicting where an object will land or maximizing profit in a business scenario. So next time you see a parabola, remember there's a world of applications behind that simple curve!

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