Question

What is the quadratic formula used for?

Answer 1

The quadratic formula is used to get the roots of a quadratic equation, if the roots exists at all.

We usually just perform factorization to get the roots of a quadratic equation. However, this is not always possible (especially when the roots are irrational)

The quadratic formula is

`x = (-b +- root 2 (b^2 - 4ac))/(2a)`

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Example 1:

`y = x^2 -3x - 4`
`0 = x^2 -3x - 4`

`=> 0 = (x - 4)(x + 1)`
`=> x = 4, x = -1`

Using the quadratic formula, let's try to solve the same equation

`x = (-(-3) +- root 2 ((-3)^2 - 4*1*(-4)))/(2 * 1)`
`=> x = (3 +- root 2 (9 + 16))/2`
`=> x = (3 +- root 2 (25))/2`
`=> x = (3 + 5)/2, x = (3 - 5)/2`
`=> x = 4, x = -1`

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Example 2:

`y = 2x^2 -3x - 5`
`0 = 2x^2 - 3x - 5`

Performing factorization is a little hard for this equation, so let's jump straight to using the quadratic formula

`x = (-(-3) +- root 2 ((-3)^2 - 4 * 2 * (-5)))/(2 * 2)`

`x = (3 +- root 2 (9 + 40))/4`

`x = (3 +- root 2 49)/4`

`x = (3 + 7)/4, x = (3 - 7)/4`

`x = 5/2, x = -1`

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