Solve 3x - 2 = x2

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Solution.

Given equation is 3x - 2 = x²

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

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

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

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

As we know, discriminant = b² - 4ac

Discriminant = (3)² - 4(-1)(-2)

Discriminant = 9 - (8)

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

=	−(3) + √1
	2(-1)

=	-3 + 1
	-2

= 1

x₂ =	−b - √D
	2a

=	−(3) - √1
	2(-1)

=	-3 - 1
	-2

= 2

Roots: x₁ = , x₂ =

Sum of roots = -b/a

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

Sum of roots = 3

Product of roots = c/a

Product of roots = (-2)/(-1)

Product of roots = 2

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