Solve 5x2 + 11x + 6 = 0

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Solution.

Given equation is 5x² + 11x + 6 = 0

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

a = 5, b = 11, c = 6

As we know, discriminant = b² - 4ac

Discriminant = (11)² - 4(5)(6)

Discriminant = 121 - (120)

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

=	−(11) + √1
	2(5)

=	-11 + 1
	10

= -1

x₂ =	−b - √D
	2a

=	−(11) - √1
	2(5)

=	-11 - 1
	10

=	-12
	10

Roots: x₁ = , x₂ =

Sum of roots = -b/a

Sum of roots = -(11)/(5)

Sum of roots = -2.2

Product of roots = c/a

Product of roots = (6)/(5)

Product of roots = 6 / 5

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