Question

solve by cardons method x3-30x+133=0​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

One root of the cubic expression $x^{3} -30x+133=0$ is

          $-7,\frac{7+3\sqrt{3} }{2} , \frac{7-3\sqrt{3} }{2}$

Step-by-step explanation:

• Since, imaginary roots occurs in pairs by using the quadratic formula we can find roots by polynomial division,

                      $x^{3} -30x+133=0$

                     $(x^{2} -7x+19)(x+7)=0$

• From $(x^{2} -7x+19)=0$, we get roots

                       $\frac{7+3\sqrt{3} }{2} , \frac{7-3\sqrt{3} }{2}$

• Now lets find real root, let real root be $=k$

              Sum of root   = $\frac{-b}{a}$ $=0$

∴ we can write as,

            $\frac{7+3\sqrt{3} }{2} + \frac{7-3\sqrt{3} }{2}+k=0$

                   $k=-7$

∴ the real root is -7