Question

3.1x^3-2.4x² +6x – 3 = 4x² + 3x +2


solving problem​

Answer 1

The roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Explanation:

The given equation is 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2

Which gives;

3.1·x³ - 2.4·x²+ 6·x - 3 - 4·x² - 3·x - 2 = 0

3.1·x³ - 6.4·x²+ 3·x - 5 = 0

Factorizing online, we get;

3.1·x³ - 6.4·x²+ 6·x + 3·x - 5 = 3.1·(x - 1.986)·(x² - 0.0784·x + 0.812) = 0

Therefore, the possible solutions are;

x - 1.986= 0 or x² - 0.0784·x + 0.812 = 0

The roots of the equation are x² - 0.0784·x + 0.812 = 0 are;

x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i

Therefore, the roots of the equation, 3.1·x³ - 2.4·x²+ 6·x - 3 = 4·x² + 3·x + 2, are;

x = 1.986, x = 0.0392 - 0.9·i, x = 0.0392 + 0.9·i.