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Solve, x2 - 8x + 15 = 0


Solution.

Given equation is x2 - 8x + 15 = 0

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

a = 1, b = -8, c = 15

As we know, discriminant = b2 - 4ac

Discriminant = (-8)2 - 4(1)(15)

Discriminant = 64 - (60)

Discriminant = 4

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          


=   −(-8) + √4
         2(1)          


=    8 + 2
         2          


= 5


x2 = −b - √D
         2a          


=   −(-8) - √4
         2(1)          


=    8 - 2
         2          


= 3


Roots: x1 = 5,     x2 = 3


Sum of roots = -b/a

Sum of roots = -(-8)/(1)

Sum of roots = 8


Product of roots = c/a

Product of roots = (15)/(1)

Product of roots = 15
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