$10+x-2{x}^{2}<0$

tikaj1x
2022-10-17
Answered

$10+x-2{x}^{2}<0$

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espava8b

Answered 2022-10-18
Author has **12** answers

We first rewrite this in standard form: $-2{x}^{2}+x+10<0$

Since the coefficient of the square is negative, we call this a "mountain"-parabola.

y=0 gives us $x=2.5\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}x=-2$

Since it's a "mountain", our answers lie outside these points, so:

$x<-2\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x>2.5$

Since the coefficient of the square is negative, we call this a "mountain"-parabola.

y=0 gives us $x=2.5\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}x=-2$

Since it's a "mountain", our answers lie outside these points, so:

$x<-2\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x>2.5$

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