Question

$x {}^{2} - \frac{3x}{10} - \frac{1}{10} = 0$
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Answer 1

$\bf solution \implies$

$x {}^{2} - \frac{3x}{10} - \frac{1}{10} = 0</p><p></p><p>$

$\therefore 10x {}^{2} - 3x - 1 = 0$

$\therefore 10x {}^{2} - 5x + 2x - 1 = 0$

$\therefore5x(2x - 1) + 1(2x - 1) = 0$

$\therefore(2x - 1)(5x + 1) = 0$

$\therefore2x - 1 = 0 \: or \: 5x + 1 = 0$

$\therefore2x = 1 \: \: \: \: or \: 5x - 1$

$\therefore x = \frac{1}{2} \: \: \: \: or \: x = - \frac{1}{5}$

$\bf ans.\frac{1}{2}, - \frac{1}{5} \: are \: the \: roots \: of \ \\ \bf the \: given \: quadratic \: equation$

Answer 2

GIVEN :-

$\\ \sf {x}^{2} - \dfrac{3x}{10} - \dfrac{1}{10} = 0$

HOW TO SOLVE :-

• The given equation is in fraction which is complicated to solve. So , we will simplify the equation by removing the denominator . We will multiply both sides by 10 . And then we can easily solve the equation by splitting middle term.

SOLUTION :-

We have ,

$\\ \sf \: {x}^{2} - \dfrac{3x}{10} - \dfrac{1}{10} = 0$

Multiplying both sides by 10 , we get...

$\\ \sf \implies \: 10 \left( {x}^{2} - \dfrac{3x}{10} - \dfrac{1}{10} \right) = 10(0) \\ \\ \\ \sf \implies \: \underline{10 {x}^{2} - 3x - 1 = 0}$

Now we will solve the equation by splitting middle term.

$\\ \implies \sf \: \underline{10 {x}^{2} - 5x }+ \underline{2x - 1} = 0$

Taking common factor , we get..

$\\ \implies \sf \: 5x(2x - 1) + 1(2x - 1) = 0 \\ \\ \implies \sf \:(5x + 1)(2x - 1) = 0$

By Zero Product Property,

If a×b = 0 , then a = 0 or b = 0

Hence ,

$\sf \: 5x + 1 = 0 \: \: \: \: \: \: or \: \: \: \: \: \: \: 2x - 1 = 0 \\ \\ \sf 5x = - 1 \: \: \: \: \: \: or \: \: \: \: \: \: 2x = - 1 \\ \\ \therefore \boxed{ \sf \:x = \frac{ - 1}{5}} \: \: \: \: \: \: \sf or \: \: \: \: \: \boxed{ \sf x = \frac{1}{2} }$