Solve 3p2 -5p = 2

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Solution.

Given equation is 3p² -5p = 2

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

3p² -5p = 2 converted into 3x² - 5x - 2 = 0

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

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

As we know, discriminant = b² - 4ac

Discriminant = (-5)² - 4(3)(-2)

Discriminant = 25 - (-24)

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

=	−(-5) + √49
	2(3)

=	5 + 7
	6

= 2

x₂ =	−b - √D
	2a

=	−(-5) - √49
	2(3)

=	5 - 7
	6

=	-2
	6

Roots: x₁ = 2, x₂ = -1/3

Sum of roots = -b/a

Sum of roots = -(-5)/(3)

Sum of roots = 1.6666666666667

Product of roots = c/a

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

Product of roots = -2 / 3

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