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Solve, x2 - 5x + 6 = 0


Solution.

Given equation is x2 - 5x + 6 = 0

Comparing it with the standard Form of Quadratic Equation ax2 + bx + c = 0

a = 1, b = -5, c = 6

As we know, discriminant = b2 - 4ac

Discriminant = (-5)2 - 4(1)(6)

Discriminant = 25 - (24)

Discriminant = 1

Since discriminant > 0
Both roots are real and unequal.

Using quadratic formula


Roots(x1, x2) = −b ± √   b2 − 4ac 
         2a          


Roots(x1, x2) = −b ± √ D
         2a          


x1 = −b + √D
         2a          


=   −(-5) + √1
         2(1)          


=    5 + 1
         2          


= 3


x2 = −b - √D
         2a          


=   −(-5) - √1
         2(1)          


=    5 - 1
         2          


= 2


Roots: x1 = 3,     x2 = 2


Sum of roots = -b/a

Sum of roots = -(-5)/(1)

Sum of roots = 5


Product of roots = c/a

Product of roots = (6)/(1)

Product of roots = 6
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