The roots of the equation 4 x 2-24 x 3-57 x 2-18 x -45-0 if one of them is 3- i -6- areA- 3-i -6- -3-2-3-2C- 3-i -6- -3-2D- None of these

The correct option is C x^2 – 6x + 15 = 0 is quadratic corresponding to roots 3 ± i√(6) and dividing the given equation by this, we get 4x^2 3=0 ⇒ x=±√(3)/2 ...

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Standard XII

Mathematics

Higher Order Equations

The roots of ...

Question

The roots of the equation $4 x^{2} - 24 x^{3} + 57 x^{2} + 18 x - 45 = 0$ if one of them is $3 + i \sqrt{6}$ , are

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Solution

The correct option is C

$x^{2}$ – 6x + 15 = 0 is quadratic corresponding to roots $3 \pm i \sqrt{6}$ and dividing the given equation by this, we get $4 x^{2} - 3 = 0 \Rightarrow x = \pm \frac{\sqrt{3}}{2}$

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The roots of the equation 4x2−24x3+57x2+18x−45=0 if one of them is 3+i√6 , are

The correct option is C x2 – 6x + 15 = 0 is quadratic corresponding to roots 3±i√6 and dividing the given equation by this, we get 4x2−3=0⇒x=±√32

The roots of the equation $4 x^{2} - 24 x^{3} + 57 x^{2} + 18 x - 45 = 0$ if one of them is $3 + i \sqrt{6}$ , are

The correct option is C

$x^{2}$ – 6x + 15 = 0 is quadratic corresponding to roots $3 \pm i \sqrt{6}$ and dividing the given equation by this, we get $4 x^{2} - 3 = 0 \Rightarrow x = \pm \frac{\sqrt{3}}{2}$