Question

3x³+5x²+4x+1 can anyone answer this??​

Answer 1

let, f(x)= 3x³+5x²+4x+1=0

Then, Discriminant[f(x),x], Δ = –31 < 0

Thus, x₁ ∈ ℝ and x₂,₃ ∉ ℝ

$f(x) ≡(x+\frac{5}{9})^{3} +(x+\frac{5}{9})\frac{11}{27} -\frac{47}{729} =0$

Then, using the cubic formula, we get the three roots as :

$x_{1} = \frac{ - 10 + \sqrt[3]{188 + 36 \sqrt{93} } + \sqrt[3]{188 - 36 \sqrt{93} } }{18}$

$x_{2, 3} = \frac{ - 20 - \sqrt[3]{188 + 36 \sqrt{93} } - \sqrt[3]{188 - 36 \sqrt{93} } + i\sqrt{3} (± \sqrt[3]{  188 + 36 \sqrt{93}  } ∓  \sqrt[3]{188 - 36 \sqrt{93} }) }{36}$

where, i = √(–1)