If one root of the cubic equation x3-30 x-133-0 is 7-3 -3 i-2- Find the real root of the cubic equation-

Since, Imaginary roots occurs in pairs Other root is nbsp;7 3 √(3)i/2 Let's real root is k. Sum of the root = nbsp; b/a= 0 7+3 √(3)i/2 nbsp;+ nbsp;7 3 ...

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Standard XII

Mathematics

Higher Order Equations

If one root o...

Question

If one root of the cubic equation $x^{3} - 30 x + 133 = 0 i s \frac{7 + 3 \sqrt{3} i}{2}$ . Find the real root of the cubic equation.

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Solution

Since, Imaginary roots occurs in pairs

Other root is $\frac{7 - 3 \sqrt{3} i}{2}$

Let's real root is k.

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

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

k = -7, So, real root is -7

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If one root of the cubic equation x3−30x+133=0is7+3√3i2. Find the real root of the cubic equation. __

Since, Imaginary roots occurs in pairs Other root is 7−3√3i2 Let's real root is k. Sum of the root = −ba=0 7+3√3i2+7−3√3i2+k=0 k = -7, So, real root is -7

If one root of the cubic equation $x^{3} - 30 x + 133 = 0 i s \frac{7 + 3 \sqrt{3} i}{2}$ . Find the real root of the cubic equation.

__

Since, Imaginary roots occurs in pairs

Other root is $\frac{7 - 3 \sqrt{3} i}{2}$

Let's real root is k.

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

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

k = -7, So, real root is -7