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Complex Numbers and Quadratic Equations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSComplex Numbers and Quadratic Equations3 Marks
Question
Solve: 27x2 - 10x+ 1 = 0
✓

Answer

Here 27x2 - 10x + 1 = 0
Comparing the given quadratic equation with ax2 + bx + c = 0 we have,
a = 27, b = - 10 and c = 1
$x = \frac{{ - ( - 10) \pm \sqrt {{{( - 10)}^2} - 4 \times 27 \times 1} }}{{2 \times 27}}$
$ = \frac{{10 \pm \sqrt {100 - 108} }}{{54}} = \frac{{10 \pm 2\sqrt 2 i}}{{54}}$
$ = \frac{{5 \pm \sqrt 2 i}}{{27}}$
Thus $x = \frac{{5 + \sqrt 2 i}}{{27}}$ and $x = \frac{{5 - \sqrt 2 i}}{{27}}$

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