Subjects algebra

Three Roots 085D5B

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Three Roots 085D5B


1. The problem is to find the three answers, which typically means solving a cubic equation or finding three roots of a given problem. 2. If the problem is to solve a cubic equation $ax^3 + bx^2 + cx + d = 0$, we use the cubic formula or factorization methods. 3. Important rules: A cubic equation has three roots (real or complex). The sum of roots is $-\frac{b}{a}$, the product is $-\frac{d}{a}$. 4. Without a specific equation, let's consider an example: Solve $x^3 - 6x^2 + 11x - 6 = 0$. 5. Factor the polynomial: Try possible roots using Rational Root Theorem: 1, 2, 3. 6. Test $x=1$: $1 - 6 + 11 - 6 = 0$, so $x=1$ is a root. 7. Divide polynomial by $(x-1)$: Quotient is $x^2 - 5x + 6$. 8. Factor $x^2 - 5x + 6 = (x-2)(x-3)$. 9. So roots are $x=1$, $x=2$, and $x=3$. 10. Final answers: $\boxed{1, 2, 3}$.