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

1 Answer

Jun 19, 2018

$K = - 16$ $K=-16$

Explanation:

$K = x^{2} - 8 x xxx \to xxx x^{2} - 8 x - K$ $K=x^2-8xcolor(white)("xxx")rarrcolor(white)("xxx")x^2-8x-K$

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

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

$XXXXXXXXXXXXXXXXX \Rightarrow + a^{2} = 16$ $color(white)("XXXXXXXXXXXXXXXXX")rArr+a^2=16$

$XXXXXXXXXXXXXXXXX \Rightarrow - K = 16$ $color(white)("XXXXXXXXXXXXXXXXX")rArr-K=16$

$XXX \Rightarrow K = - 16$ $color(white)("XXX")rArrK=-16$

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