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Solve, -9x2 + 4x2 + 2x + 7 = 0


Solution.

Given equation is -9x2 + 4x2 + 2x + 7 = 0

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

a = -5, b = 2, c = 7

As we know, discriminant = b2 - 4ac

Discriminant = (2)2 - 4(-5)(7)

Discriminant = 4 - (-140)

Discriminant = 144

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          


=   −(2) + √144
         2(-5)          


=    -2 + 12
         -10          


= -1


x2 = −b - √D
         2a          


=   −(2) - √144
         2(-5)          


=    -2 - 12
         -10          


=    -14
   -10    


Roots: x1 = ,     x2 =


Sum of roots = -b/a

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

Sum of roots = 0.4


Product of roots = c/a

Product of roots = (7)/(-5)

Product of roots = 7 / -5
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