Quadratic Equations, its Sum and Product|| don't know how to do it follow our ride.

 ax² + bx + c = 0 blogger and contributor.

-b/a for sum

c/a for product

The almighty formulae of quadratic equation is given by the following

-b+or- (√b² - √4ac)/2a

Find the Sum and Product of the root of each of the following.

2x² + 3x - 1 = 0

3x² - 5x -2 = 0

x² - 4x - 3 = 0

x²/2 - 3x - 1 = 0

Example 1

The formulae for sum is given by (α+β) and for the sum is given by (αβ)

2x² + 3x - 1 = 0

a = 2 , b = 3, c = 1

α+β = -b/a = -3/2  

αβ = -1/2

Example 2

3x² - 5x - 2 = 0

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

(α + β) = -b/a = -(-5)/3 = 5/3

(αβ) = c/a = -2/3

Remember alpha(α) and beta(β) is x² - (α+β)x + αβ = 0

Also Note that: 

(α+β)² = α² + 2αβ + β²

(α+β)² - 2αβ = α² + β²

Therefore α² + β² = (α + β)² - 2αβ

α³ + β³ = (α + β)³ = α³ + 3α²β² + β³

= α³ + β³ + 3αβ(α + β)

Please later we shall update the post with the proof on how the sum and Product was derived.