4-1.Complex numbers
medium

ઉકેલો : $21 x^{2}-28 x+10=0$

A

$\frac{2}{3} \pm \frac{\sqrt{14}}{21}$

B

$\frac{2}{3} \pm \frac{\sqrt{14}}{21}$

C

$\frac{2}{3} \pm \frac{\sqrt{14}}{21}$

D

$\frac{2}{3} \pm \frac{\sqrt{14}}{21}$

Solution

The given quadratic equation is $21 x^{2}-28 x+10=0$

On comparing this equation with $a x^{2}+b x+c=0,$

we obtain $a=21, b=-28$ and $c=10$

Therefore, the discriminant of the given equation is

$D=b^{2}-4 a c=(-28)^{2}-4 \times 21 \times 10=784-840=-56$

Therefore, the required solutions are

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-(-28) \pm \sqrt{-56}}{2 \times 21}=\frac{28 \pm \sqrt{56} i}{42} \quad[\sqrt{-1}=i]$

$=\frac{28 \pm 2 \sqrt{14} i}{42}=\frac{28}{42} \pm \frac{2 \sqrt{14}}{42} i=\frac{2}{3} \pm \frac{\sqrt{14}}{21} i$

Standard 11
Mathematics

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