If $A_{1} x^{3} + A_{2} x^{2} + A_{3} x + A_{4} = 0$ $A_1x^3+A_2x^2+A_3x+A_4=0$ Can be simplified Down to $a_{1} x^{2} + a_{2} x + a_{3} = 0$ $a_1x^2+a_2x+a_3=0$ , what are the Values of $a_{1}, a_{2}, a_{3}$ $a_1,a_2,a_3$ ?

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Answer 1 · 2018-03-07T14:51:22

See the explanation below

We need

$(x^n)'=nx^(n-1)$

$A_1x^3+A_2x^2+A_3x+A_4=0$

Calculate the derivative

$(A_1x^3+A_2x^2+A_3x+A_4)'=0$

$3A_1x^2+2A_2x+A_3=0$

Comparing this to

$a_1x^2+a_2x+a_3=0$

Therefore,

$a_1=3A_1$

$a_2=2A_2$

$a_3=A_3$

If A_1x^3+A_2x^2+A_3x+A_4=0A1x3+A2x2+A3x+A4=0A_1x^3+A_2x^2+A_3x+A_4=0 Can be simplified Down to a_1x^2+a_2x+a_3=0a1x2+a2x+a3=0a_1x^2+a_2x+a_3=0, what are the Values of a_1,a_2,a_3a1,a2,a3a_1,a_2,a_3?