Solve 9x2 = 25 + 8x2

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Solution.

Given equation is 9x² = 25 + 8x²

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

9x² = 25 + 8x² converted into x² + 0x - 25 = 0

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

a = 1, b = 0, c = -25

As we know, discriminant = b² - 4ac

Discriminant = (0)² - 4(1)(-25)

Discriminant = 0 - (-100)

Discriminant = 100

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

=	−(0) + √100
	2(1)

=	0 + 10
	2

= 5

x₂ =	−b - √D
	2a

=	−(0) - √100
	2(1)

=	0 - 10
	2

= -5

Roots: x₁ = -5, x₂ = 5

Sum of roots = -b/a

Sum of roots = -(0)/(1)

Sum of roots = 0

Product of roots = c/a

Product of roots = (-25)/(1)

Product of roots = -25

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