Final answer:
To solve the quadratic inequality (x-4) (x-1)<0, we need to find the values of x that make the expression less than zero. The solution is 1 < x < 4.
Step-by-step explanation:
To solve the quadratic inequality (x-4) (x-1)<0, we need to find the values of x that make the expression less than zero.
We can do this by finding the critical points of the expression, which are the values of x where the expression equals zero. The critical points are x = 4 and x = 1.
We can then plot these critical points on a number line and test intervals between the critical points to determine whether the expression is positive or negative.
Based on the number line, we find that the expression is negative when x is between 1 and 4.
Therefore, the solution to the quadratic inequality (x-4) (x-1)<0 is 1 < x < 4.