Question

K=x^2-8x What value does K have if there is only one solution?

Answer 1

`K=-16`

Explanation:

`K=x^2-8xcolor(white)("xxx")rarrcolor(white)("xxx")x^2-8x-K`

In order for a quadratic (with a unit coefficient for `x^2`) to have only one solution it must be possible to write it in the form:
`color(white)("XXX")(x-a)^2=(x^2-2ax+a^2)`

This implies that `-2ax=-8x`
`color(white)("XXXXXXXXXXXXXXXXX")rArr a=4`

`color(white)("XXXXXXXXXXXXXXXXX")rArr+a^2=16`

`color(white)("XXXXXXXXXXXXXXXXX")rArr-K=16`

`color(white)("XXX")rArrK=-16`