Question

2xsquare+2x+1/2=0
factorize the quadratic equation ​

Answer 1

Given Polynomial : 2x² + 2x + 1/2 = 0

We've to find the factorisation of given equation.

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~ To find the value of x in the quadratic equation, We need to factorize the given equation.

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☆ Let's factorise the Given Equation:

$\begin{gathered}\qquad:\implies\sf {2x}^{2} + 2x + \dfrac{1}{2}= 0\\\\\\ \qquad:\implies\sf {4x}^{2} + 2x + 2x + 1= 0\\\\\\ \qquad:\implies\sf 2x(2x + 1) + 1(2x + 1)= 0\\\\\\ \qquad:\implies\sf (2x + 1)(2x + 1) = 0 \\\\\\ \qquad:\implies\sf {(2x + 1)}^{2} = 0 \;or\; {(2x + 1)}^{2} = 0\\\\\\\qquad:\implies\sf 2x = -1\\\\\\ \qquad:\implies{\underline{\boxed{\pmb{\frak{\red{x = - \dfrac{1}{2} \:}}}}}}\:\bigstar\\\\\\\end{gathered}$

$\therefore\:{\underline{\sf{Hence,\:Value \: of \: x \:is\:{\bf {- \frac{1}{2} }}\:{\sf{\&}}\:{\bf{- \frac{1}{2} }}.}}}$

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⠀⠀⠀⠀⠀✇ $\underline{ \pmb{ \frak{ \red{Additional \: information...}}}}$

• Standard form of a quadratic equation is : a² + bc + x = 0, & a ≠ 0.

• Factoring an equation means to expand the equation and take out two common factors.

• Example - By factorising 2x² + 2x + 1/2 = 0, We get two common factors, (2x + 1)(2x + 1) = 0.