Solve -3x2 = 2x

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Solution.

Given equation is -3x² = 2x - 1

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

-3x² = 2x - 1 converted into -3x² - 2x + 1 = 0

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

a = -3, b = -2, c = 1

As we know, discriminant = b² - 4ac

Discriminant = (-2)² - 4(-3)(1)

Discriminant = 4 - (-12)

Discriminant = 16

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) + √16
	2(-3)

=	2 + 4
	-6

= -1

x₂ =	−b - √D
	2a

=	−(-2) - √16
	2(-3)

=	2 - 4
	-6

=	-2
	-6

Roots: x₁ = , x₂ =

Sum of roots = -b/a

Sum of roots = -(-2)/(-3)

Sum of roots = -0.66666666666667

Product of roots = c/a

Product of roots = (1)/(-3)

Product of roots = 1 / -3

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