Question

For what values of x,x²-5x+6 is positive​

Answer 1

Answer:

Step-by-step explanation:

x2-5x+6

(X-3)(x-2)>o

X belongs to (-infinite,2) union (3, infinite)

Answer 2

Answer:

$x^{2} -5x+6$ is positive for values $(-\infty, 2)\cup(3,\infty)$

Step-by-step explanation:

Given the expression, $x^{2} -5x+6$

To be positive, $x^{2} -5x+6 > 0$    

Finding the factors of the equation,

                                   $=x^{2} -2x-3x+6 > 0$

                                   $=x(x -2)-3(x-2) > 0$

                                   $=(x -2)(x-3) > 0$

If $x - 3 > 0$ then $x - 2 < 0$

$\implies x > 3$ or $x < 2$

Hence the range of positive values is $(-\infty, 2)\cup(3,\infty)$

Therefore the given expression is positive for a range of $(-\infty, 2)\cup(3,\infty)$.