Question

solve this cubic equation 5x³-2x²+3x-2?

Answer 1

this equation has only one real root that is 0.57 .and other are imaginary. you can check it by graph plotting of cubic polynomial.

Answer 2

To Solve

For all the values of x such that.

$f(x) = 5 {x}^{3} - 2 {x}^{2} + 3x - 2 = 0$

Calculating the discriminant of the above cubic so as to know the bature of three three roots.

$\triangle = - 2188 < 0$

$\implies x_{1} \in ℝ \: , x_{2,3} \notin ℝ$

Therefore, the only real root is given by:

$x_1= { \frac{2 + \sqrt[3]{548 + 15 \sqrt{1641} } + \sqrt[3]{548 - 15 \sqrt{1641} } }{15} }$

After approximations:

$x_1 \approx 0.572466...$