Solve x2 + 3 = 5x

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Solution.

Given equation is x² + 3 = 5x

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

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

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

a = 1, b = -5, c = 3

As we know, discriminant = b² - 4ac

Discriminant = (-5)² - 4(1)(3)

Discriminant = 25 - (12)

Discriminant = 13

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) + √13
	2(1)

=	5 + √13
	2

x₂ =	−b - √D
	2a

=	−(-5) - √13
	2(1)

=	5 - √13
	2

Roots: x₁ = , x₂ =

Sum of roots = -b/a

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

Sum of roots = 5

Product of roots = c/a

Product of roots = (3)/(1)

Product of roots = 3

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