Question

The polynomial function f has only real zeros. Find them f(x) = 4x^3 - 62.8x^2 + 67.04x + 37.12

Answer 1

\[4 x^3-62.8 x^2+67.04 x+37.12 \]
Rationalize the cooeficients.\[4 x^3-\frac{314}{5}x^2+\frac{1676}{25} x+\frac{928}{25} \]Factor the expression:\[\frac{2}{25} (2 x-29) (5 x-8) (5 x+2) \]

Answer 2

There is a simple formula for this.
Let f(x) = ax^3 + bx^2 + cx + d
The roots will be d/a , -c/a , b/a

Answer 3

\[\left\{x=-\frac{2}{5},x=\frac{8}{5},x=\frac{29}{2}\right\}\to \{x=-0.4,x=1.6,x=14.5\} \]