Solve 3x = -5 + 2x2

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Solution.

Given equation is 3x = -5 + 2x²

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

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

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

a = -2, b = 3, c = 5

As we know, discriminant = b² - 4ac

Discriminant = (3)² - 4(-2)(5)

Discriminant = 9 - (-40)

Discriminant = 49

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

=	−(3) + √49
	2(-2)

=	-3 + 7
	-4

= -1

x₂ =	−b - √D
	2a

=	−(3) - √49
	2(-2)

=	-3 - 7
	-4

=	-10
	-4

Roots: x₁ = -1, x₂ = 10/4

Sum of roots = -b/a

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

Sum of roots = 1.5

Product of roots = c/a

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

Product of roots = 5 / -2

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