If x^2 - 5x + 8 = 0  find the roots of the equartion. Are the roots real number?

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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Let f(x) = x^2 - 5x + 8 = 0

Then, we need to find the roots of the equation f(x).

First, let us calculate delta to determine if the roots are real or complex.

We know that delta = b^2 - 4ac

==> If delta < 0 , then the roots are complex.

==> If delta = 0, then the function has one real root.

==> If delta > 0 , then the function has 2 real roots.

==> delta = 25 - 4*1*8 = 25 - 32 = -7.

Then, delta <  0..

==> The function has 2 real roots.

==> x1= ( -b + sqrt(delta) / 2a

==> x1= ( 5 + sqrt(-7) /2 = (5+sqrt7*i)/2

==> x2= (5-sqrt7*i)/2

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