I'm trying to refresh myself on math, and i've come across something I can't understand.
so we have the polynomial f(x)=4x^3+3x^2-6x-1=0, and the derivative, being a quadratic, is
f'(x)=12x^2+6x-6 and apparently this has explicit solutions.
so when I try and place these values into the quadratic equation, i got a different value to the text. they got -1 and 1/2. i soon realized that the text used b and b^2 from the polynomial, and the a and c values of the quadratic.
so what's the deal? i thought if you were using a quadratic equation, you only use the first derivative of the polynomial (the quadratic), not the polynomial. is it a process of using both the equations?
thanks in advance.
note: I'm using the text "mathemaical methods for physics and engineering" 2nd edition by k.f. riley, m.p. hobson and s.j. bence. and this is page 6.