Solve this

Question:

18. $21 x^{2}-28 x+10=0$

Solution:

Given:

 $21 x^{2}-28 x+10=0$

Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\Rightarrow x=\frac{-(-28) \pm \sqrt{(-28)^{2}-(4 \times 21 \times 10)}}{2 \times 21}$

$\Rightarrow x=\frac{28 \pm \sqrt{784-840}}{42}$

$\Rightarrow x=\frac{28 \pm \sqrt{-56}}{42}$

$\Rightarrow x=\frac{28 \pm 2 \sqrt{14} i}{42}$

$\Rightarrow x=\frac{28}{42} \pm \frac{2 \sqrt{14}}{42} i$

Ans: $x=\frac{2}{3}+\frac{\sqrt{14}}{21} i$ and $x=\frac{2}{3}-\frac{\sqrt{14}}{21} i$

 

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