Question

-3x^3+7x+2x^2+2 = 0.

Answer 1

Ответ:

-9х+9х +4+2=-24

Айтып қойаиын дұрыс па білмеймін өздерің білесіңдер,жазғыларың келсе жазыңдар

Объяснение:

Сенімді емеспін

Answer 2

To solve the equation -3x^3 + 7x + 2x^2 + 2 = 0, you can follow these steps:

1. Rearrange the terms in descending order of the exponent (highest to lowest): -3x^3 + 2x^2 + 7x + 2 = 0

2. Try to factor out common terms, if possible. In this case, there are no common factors among the terms.

3. Next, you can attempt to use the Rational Root Theorem to find potential rational roots (solutions) of the equation. The Rational Root Theorem states that if there is a rational root p/q (where p and q are integers with no common factors, and q is not equal to 0) for a polynomial equation, then p must divide the constant term (in this case, 2), and q must divide the leading coefficient (in this case, -3).

   The potential rational roots for this equation are: p = ±1, ±2 q = ±1, ±3

4. Now, you can test these potential roots one by one using synthetic division or direct substitution to see if they are actual roots of the equation.

   Let's start with p = 1: -3(1)^3 + 2(1)^2 + 7(1) + 2 = -3 + 2 + 7 + 2 = 8

   The result is not equal to 0, so x = 1 is not a root.

   Next, try p = -1: -3(-1)^3 + 2(-1)^2 + 7(-1) + 2 = 3 + 2 - 7 + 2 = 0

   The result is equal to 0, so x = -1 is a root.

5. Now that you've found one root (x = -1), you can perform polynomial division or synthetic division to factor out the quadratic equation. Divide the original cubic equation by (x + 1) to get the quadratic equation:

   (-3x^3 + 2x^2 + 7x + 2) / (x + 1) = -3x^2 + 5x + 2

6. Now, solve the quadratic equation -3x^2 + 5x + 2 = 0. You can factor it or use the quadratic formula:

   -3x^2 + 5x + 2 = 0

   To factor, you can find two numbers that multiply to -6 (the product of the leading coefficient and the constant term) and add up to 5 (the coefficient of the linear term). Those numbers are 6 and -1.

   -3x^2 + 6x - x + 2 = 0

   -3x(x - 2) - 1(x - 2) = 0

   (x - 2)(-3x - 1) = 0

   Set each factor equal to 0:

   x - 2 = 0 --> x = 2 -3x - 1 = 0 --> -3x = 1 --> x = -1/3

So, the solutions to the original equation -3x^3 + 7x + 2x^2 + 2 = 0 are: x = -1 x = -1/3 x = 2