Question

Is x2 + x= 2 a linear equation? Justify?

Answer 1

${x}^{2} + x = 2$

This equation is not linear because of the following reasons :

1. In a linear equation degree of the polynomial/equation must be 1 but it is not 1 in this equation it is 2.
2. And the most important thing of an equation is that it is always equal to zero but this equation is not equal to zero that's why it is not an equation.
3. A Linear equation has only 1 root, but as we can see clearly this is an quadratic equation and hence it has 2 roots, and it's roots can be calculated easily by Shri Dhara Charya formula.

${x}^{2} + x = 2 \\ {x}^{2} + x - 2 = 0 \\ \frac{ - b + or - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \frac{ - 1 + - \sqrt{1 - ( - 2)(4)(1)} }{2} \\ \frac{ - 1 + - \sqrt{1 - ( - 8)} }{2} \\ \frac{ - 1 + - \sqrt{9} }{2} \\ \frac{ - 1 + - 3}{2} \\ it \: has \: two \: roots \\ \frac{ - 1 + 3}{2} = 1 \: \: and \: \frac{ - 1 - 3}{2} = - 2 \\ so \: the \: roots \: are \: + 1 \: and \: - 2.$

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