Answer:
solving the inequality: [tex]x^2+x-2\geq 0[/tex] we get [tex]\{x|x\leq -2 \ or \ x\geq 1\}\\[/tex]
Option A is correct option
Step-by-step explanation:
We need to solve the inequality: [tex]x^2+x-2\geq 0[/tex]
We can solve using factors:
[tex]x^2+x-2\geq 0[/tex]
We will break the middle term, in such way that their sum is equal to middle term and product is equal to product of first and last term.
[tex]x^2+x-2\geq 0\\x^2+2x-x-2\geq 0\\x(x+2)-1(x+2)\geq 0\\(x-1)(x+2)\geq 0\\x-1\geq 0 \ or \ x+2\geq 0\\x\geq1 \ or \ x\leq-2\\[/tex]
So, solving the inequality: [tex]x^2+x-2\geq 0[/tex] we get [tex]\{x|x\leq -2 \ or \ x\geq 1\}\\[/tex]
Option A is correct option
