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  • Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (ii) 2x ^2 + x - 4 = 0

Q1.    Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

                (ii)    2x^2 + x -4 = 0

Answers (1)

best_answer

Given equation: 2x^2 + x -4 = 0

On dividing both sides of the equation by 2, we obtain

\Rightarrow x^2+\frac{1}{2}x-2 = 0

Adding and subtracting  \frac{1}{16}  in the equation, we get

\Rightarrow (x+\frac{1}{4})^2 -2 - \frac{1}{16} = 0

\Rightarrow (x+\frac{1}{4})^2 =2+\frac{1}{16}

\Rightarrow (x+\frac{1}{4})^2 = \frac{33}{16}

\Rightarrow (x+\frac{1}{4}) =\pm \frac{\sqrt{33}}{4}

\Rightarrow x =\pm \frac{\sqrt{33}}{4} -\frac{1}{4}

\Rightarrow x = \frac{\pm \sqrt{33} - 1}{4}

\Rightarrow x = \frac{ \sqrt{33} - 1}{4}\ or\ x = \frac{ -\sqrt{33} - 1}{4}

 

 

Posted by

Divya Prakash Singh

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