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Solve, x2 - 3x = 2x


Solution.

Given equation is x2 - 3x = 2x

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

x2 - 3x = 2x converted into x2 - 5x + 0 = 0

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

a = 1, b = -5, c = 0

As we know, discriminant = b2 - 4ac

Discriminant = (-5)2 - 4(1)(0)

Discriminant = 25 - (0)

Discriminant = 25

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) + √25
         2(1)          


=    5 + 5
         2          


= 5


x2 = −b - √D
         2a          


=   −(-5) - √25
         2(1)          


=    5 - 5
         2          


= 0


Roots: x1 = 0,     x2 = 5


Sum of roots = -b/a

Sum of roots = -(-5)/(1)

Sum of roots = 5


Product of roots = c/a

Product of roots = (0)/(1)

Product of roots = 0
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