Question

Quantas soluções inteiras temos na inequação –x2 – 3x + 10 ≥ 0 no intervalo?

a)5

b)6

c)7

d)8

e)9​

Answer 1

$-x^2-3x+10\geq 0\\x^2+3x-10\leq 0\\\Delta =9-4.1.(-10)=49\\x= \frac{-3\pm 7}{2}\Rightarrow x_1\leq 2 \ ou \ x_2\geq -5\\\\S=\left \{ x\in \mathbb{Z}: -5\leq x\leq 2\left. \right \} \right.\\S=\left \{ -5,-4,-3,-2,-1,0,1,2\left. \right \} \right.\Rightarrow n(S)=8$