Solve this

Question:

$25 x^{2}-30 x+11=0$

 

Solution:

 Given:

$25 x^{2}-30 x+11=0$

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

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

$\Rightarrow x=\frac{-(-30) \pm \sqrt{(-30)^{2}-(4 \times 25 \times 11)}}{2 \times 25}$

$\Rightarrow x=\frac{30 \pm \sqrt{900-1100}}{50}$

$\Rightarrow x=\frac{30 \pm \sqrt{-200}}{50}$

$\Rightarrow x=\frac{30 \pm 10 \sqrt{2} i}{50}$

$\Rightarrow x=-\frac{30}{50} \pm \frac{10 \sqrt{2}}{50} i$

Ans: $x=-\frac{3}{5}+\frac{\sqrt{2}}{5} i$ and $x=-\frac{3}{5}-\frac{\sqrt{2}}{5} i$

 

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