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Solve, 2x2 + 11 = x2 + 12


Solution.

Given equation is 2x2 + 11 = x2 + 12

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

2x2 + 11 = x2 + 12 converted into x2 + 0x - 1 = 0

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

a = 1, b = 0, c = -1

As we know, discriminant = b2 - 4ac

Discriminant = (0)2 - 4(1)(-1)

Discriminant = 0 - (-4)

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          


=   −(0) + √4
         2(1)          


=    0 + 2
         2          


= 1


x2 = −b - √D
         2a          


=   −(0) - √4
         2(1)          


=    0 - 2
         2          


= -1


Roots: x1 = -1,     x2 = 1


Sum of roots = -b/a

Sum of roots = -(0)/(1)

Sum of roots = 0


Product of roots = c/a

Product of roots = (-1)/(1)

Product of roots = -1
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