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Solve, x2 + 1 = -2x


Solution.

Given equation is x2 + 1 = -2x

Converting given equation into Standard Form of Quadratic Equation. ax2 + bx + c = 0

x2 + 1 = -2x converted into x2 + 2x + 1 = 0

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

a = 1, b = 2, c = 1

As we know, discriminant = b2 - 4ac

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

Discriminant = 4 - (4)

Discriminant = 0

Since discriminant = 0
Both roots are real and equal.

Using quadratic formula


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


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


x1 = −b + √D
         2a          


=   −(2) + √0
         2(1)          


=    -2 + 0
         2          


= -1


x2 = −b - √D
         2a          


=   −(2) - √0
         2(1)          


=    -2 - 0
         2          


= -1


Roots: x1 = -1,     x2 = -1


Sum of roots = -b/a

Sum of roots = -(2)/(1)

Sum of roots = -2


Product of roots = c/a

Product of roots = (1)/(1)

Product of roots = 1
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