Question

How do you solve `3x² – 16x + 5 = 0`?

Answer 1

`x = 5` or `x = 1/3`

Explanation:

Factorise into `(3x-1)(x -5) = 0`

For the left hand side to be zero, the contents of one of the brackets must evaluate to zero, hence

`3x - 1 = 0 implies x = 1/3`

or

`x - 5 = 0 implies x = 5`.

Alternatively you can use the quadratic formula for equations of the from `ax^2 + bx + c = 0`

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

So in this case, a = 3, b = -16 and c = 5.

`x = (16 + sqrt(256 - 60))/6` or `(16 - sqrt(256 - 60))/6`

`therefore x = 5 or x = 1/3`

Answer 2

`1/3 and 5`

Explanation:

Another way is to use the Transforming Method (Google, Yahoo Search)
`y = 3x^2 - 16x + 5`.
Find the real roots of the transformed equation:
`y' = x^2 - 16x + 15`.
Since a + b + c = 0, use shortcut, the 2 real roots are: X1 = 1 and
`X2 = c/a = 15`.
Back to original equation y, the 2 real roots are: `x1 = (X1)/a = 1/3`
and `x2 = (X2)/a = 15/3 = 5.`