blue powder
Registered User

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.

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.

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## Posts

If you are trying to find the zeros of f'(x) then yes, the answer is -1 and 1/2.

edit: just to clarify "f(x)=4x^3+3x^2-6x-1=0" doesn't make sense. You have a function f(x) which is 4x^3+3x^2-6x-1. At some points a function may be equal to zero. To find these points you use the equality 4x^3+3x^2-6x-1=0. f(x)=0 implies the function is always zero which is obviously not the case.

.kbf?onPi-r8onblue powderon-6 +- sqrt(6^2 - (4*12*-6))/2*12

-6 +- sqrt(36 - (-288))/24

-6 +- 18 /24

equals -24/24 and 12/24

simplifies to -1 and 1/2

GenericFanonThank you all for your time and help!

blue powderonEdit: nevermind, looks like you found out what was wrong.

Savanton