Question

A root of an equation which does not satisfy the equation is called

Answer 1

Answer:

A root of an equation which does not satisfy the equation is called it is not a root of that the equation.

Answer 2

Concept : A value that is determined for an unknown in the solution of an equation but is not the equation's root is referred to as a "extraneous root." It should be noted that extraneous roots are typically not defined by textbook authors. Additionally, the definition provided above is flawed because it leaves out important details.

Only two circumstances result in superfluous roots are the "square both sides" circumstance (to get rid of a square root symbol) and the "half absolute value expansion circumstance" (in order to eliminate taking absolute value). √x=x-2 is an illustration of the former, and |2x-1|=3x+6 is an illustration of the latter. In the first instance, we acquire the roots of 1 and 4 by squaring both sides, and closer examination indicates that 1 is superfluous. (Of fact, increasing both sides to a positive even power is a specific instance of squaring both sides.) In the second scenario, we divide the equation into two parts, |2x-1|=3x+6 and 2x-1= - (3x+6), yielding roots of 1 and 7, and closer examination reveals that 7.

Solution: A root of an equation which does not satisfy the equation is called extraneous solution.

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