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Solve, x2 - 7x + 12 = 0


Solution.

Given equation is x2 - 7x + 12 = 0

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

a = 1, b = -7, c = 12

As we know, discriminant = b2 - 4ac

Discriminant = (-7)2 - 4(1)(12)

Discriminant = 49 - (48)

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          


=   −(-7) + √1
         2(1)          


=    7 + 1
         2          


= 4


x2 = −b - √D
         2a          


=   −(-7) - √1
         2(1)          


=    7 - 1
         2          


= 3


Roots: x1 = 4,     x2 = 3


Sum of roots = -b/a

Sum of roots = -(-7)/(1)

Sum of roots = 7


Product of roots = c/a

Product of roots = (12)/(1)

Product of roots = 12
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