Question

What are the zeroes of the quadratic function `8x ^ { 2} - 16x - 15`?

Answer 1

`x = 1+-sqrt(46)/4`

Explanation:

We can find the zeros by completing the square:

`0 = 2(8x^2-16x-15)`

`color(white)(0) = 16x^2-32x-30`

`color(white)(0) = (4x)^2-2(4x)(4)+4^2-46`

`color(white)(0) = (4x-4)^2-(sqrt(46))^2`

`color(white)(0) = ((4x-4)-sqrt(46))((4x-4)+sqrt(46))`

`color(white)(0) = (4x-4-sqrt(46))(4x-4+sqrt(46))`

`color(white)(0) = 16(x-1-sqrt(46)/4)(x-1+sqrt(46)/4)`

Hence:

`x = 1+-sqrt(46)/4`