Question

Determine the solution set of the inequality x^(2)-3x-10>0

Answer 1

solution:

given; x²-3x-10 > 0

$\implies$ x²-5x+2x-10 > 0

$\implies$ x(x-5)+2(x-5) > 0

$\implies$ (x+2)(x-5) > 0

case - $\Iota$

(x+2) > 0 & (x-5) > 0

x > -2 & x > 5

thus the common solution is x > 5

case - $\Iota$ $\Iota$

(x+2) < 0 & (x-5) < 0

x < -2 & x < 5

thus the common solution is x < -2

hence,

using case - I and case - II we get x lies in ( -$\infty$ ,-2) $\bigcup$ (5,$\infty$ )

solution set : { x | x$\in$ ( -$\infty$ ,-2) $\bigcup$ (5,$\infty$ ) }