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Roots of an equation


The elements of the truth set of an equation are called roots of the equation. To check if a number is root of an equation, we must follow the following sequence:

  • Replace the unknown with this number.

  • Determine the value of each member of the equation.

  • Check for equality. Being a true sentence, the number considered is the root of the equation.

Examples:

Check which of the elements of the universe set are roots of the equations below, determining in each case the truth set.

  • Solve the equation x - 2 = 0, being U = {0, 1, 2, 3}.

For x = 0, we have: 0 - 2 = 0 => -2 = 0. (F)

For x = 1, we have: 1 - 2 = 0 => -1 = 0. (F)

For x = 2, we have: 2 - 2 = 0 => 0 = 0. (V)

For x = 3, we have: 3 - 2 = 0 => 1 = 0. (F)

We find that 2 is root of the equation x - 2 = 0, so V = {2}.

  • Solve the equation 2x - 5 = 1, being U = {-1, 0, 1, 2}.

For x = -1, we have: 2. (-1) - 5 = 1 => -7 = 1. (F)

For x = 0, we have: 2. 0 - 5 = 1 => -5 = 1. (F)

For x = 1, we have: 2. 1 - 5 = 1 => -3 = 1. (F)

For x = 2, we have: 2. 2 - 5 = 1 => -1 = 1. (F)

Equation 2x - 5 = 1 has no root in U, soon V = Ø.

Next: Solve an Equation