x^2 - 3x + 2 = 0


a) Determine and explain patterns in the roots.

Expert Answers

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You need to evaluate the two roots to the given quadratic equation, hence, either you may use quadratic formula, or you may use factorization, or you may complete the square.

Using quadratic formula, yields:

`x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)`

a,b,c represent the coefficients of equation `ax^2 + bx + c = 0`

Identifying the coefficients yields:

`a = 1, b = -3, c = 2`

`x_(1,2) = (3 +- sqrt(9 - 8))/2 => x_(1,2) = (3 +- 1)/2`

`x_1 = (3+1)/2 => x_1 = 2`

`x_2 = (3 - 1)/2 =>x_2 = 1`

You need to notice that an equation has as many roots as its order indicates, hence, a quadratic equation cannot have more than two roots.

Hence, evaluating the quadratic equation yields `x = 1, x = 2.`

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