- Home
- Standard 11
- Mathematics
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