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Univariate cubic equation - relationship between root and coefficient
2022-07-06 21:37:00 【m0_ sixty-six million eight hundred and seventeen thousand two 】
a x 3 + b x 2 + c x + d = 0 ax^3+bx^2+cx+d=0\\ ax3+bx2+cx+d=0 set up ： ( x − x 1 ) ( x − x 2 ) ( x − x 3 ) = 0 set up ： (x-x_1)(x-x_2)(x-x_3)=0\\ set up ：(x−x1)(x−x2)(x−x3)=0 { x 1 + x 2 + x 3 = − b a x 1 x 2 + x 2 x 3 + x 3 x 1 = c a x 1 x 2 x 3 = d a \left\{ \begin{aligned} &x_1+x_2+x_3&=&-\frac{b}{a}\\ &x_1x_2+x_2x_3+x_3x_1&=&\frac{c}{a}\\ &x_1x_2x_3&=&\frac{d}{a}\\ \end{aligned} \right. ⎩⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎧x1+x2+x3x1x2+x2x3+x3x1x1x2x3===−abacad
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