Solve the following quadratic equation. x^2-3 x 10 -1 10 =0 - Vidyadip

Question

Solve the following quadratic equation.
$x^2-\frac{3 x}{10}-\frac{1}{10}=0$

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Answer

$\begin{array}{l}10 x^2-3 x-1=0 \\ \Rightarrow 10 x^2-3 x-1=0 \text { compare with } a x^2+b x+c=0 \\ \Rightarrow a=10, b=-3 \text { and } c=-1 \\ \therefore b^2-4 a c=-3^2-4(10)(-1) \\ =9+40 \\ =49 \\ x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\end{array}$
$\begin{array}{l}\Rightarrow x =\frac{3 \pm \sqrt{49}}{2 \times 10} \\ \Rightarrow x =\frac{3 \pm 7}{20} \\ \Rightarrow x =\frac{3+7}{20} \text { or } x =\frac{3-7}{20} \\ \Rightarrow x =\frac{10}{20} \text { or } x =\frac{-4}{20} \\ \Rightarrow x =\frac{1}{2} \text { or } x =-\frac{1}{5}\end{array}$

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