Math, asked by Gomisan, 1 year ago

solve for x:3(x^3)-2(x^2)+5x=6

Mirai: Is the minus sign correct coz im not getting the ans so can check the question :-) :-)

Gomisan: yes,hint:one value of x is 1.Find the others

Gomisan: =3-2+5=6

Mirai: You know it!!! B-) :O

Answers

Answered by kvnmurty

$3x^3-2x^2+5x - 6 = 0\ \ \ \ \ - equation\ 1\\ \\ As\ odd\ terms\ add\ up\ to\ even\ terms\ (coefficients), x = 1\ is\ a\ root. \\ \\ (x-1)(3x^2+ax+6) = 0\\ \\ coefficient\ of\ x^2\ term\ is = -3+a = -2\ \ in\ equation\ 1. \\ \\ So,\ \ a = 1\\ \\ Check\ coefficient\ of\ x^1\ term: \\. \ \ \ \ \ -a+6 = -1+6 = 5,\ \ \ matches\ equation 1 \\ \\3x^2+x+6 = 0 \\ \\x = \frac{-1+-\sqrt{1-72}}{6}\\ \\ Roots\ are :\\ \\ x = 1 (real),\ Imaginary:\ \frac{-1+\sqrt{71}j}{6}, \ and\ \frac{-1-\sqrt{71}j}{6}.$

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