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Solve, 2x2 + 5x + 3 = 0


Solution.

Given equation is 2x2 + 5x + 3 = 0

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

a = 2, b = 5, c = 3

As we know, discriminant = b2 - 4ac

Discriminant = (5)2 - 4(2)(3)

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(2)          


=    -5 + 1
         4          


= -1


x2 = −b - √D
         2a          


=   −(5) - √1
         2(2)          


=    -5 - 1
         4          


=    -6
   4    


Roots: x1 = -1,     x2 =
?3
   2    

Sum of roots = -b/a

Sum of roots = -(5)/(2)

Sum of roots = -2.5


Product of roots = c/a

Product of roots = (3)/(2)

Product of roots = 3 / 2
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