First, factorise the x terms.
To find the roots:
The question asks us to find the portion of the curve which is less than zero . Thus, we need to show by giving a range of values of x.
Do a rough sketch of a graph showing
curve on x and y axis
- curve must be positive, meaning it has a minimum point. (like a smile)
- label the x-intercepts with the values found above.
Since the equality given is "<", draw a small circle at the intercepts.
The portion of the curve that is negative falls below
This means the curve is negative between and
Which is expressed as
(If the question states , the portions of the curve that are positive is when and )
Explanation the quadratic on the left side
find the zeros
These indicate where the function changes sign
the zeros split the x-axis into 3 intervals
Consider a test point in each interval
we want to find where the function is negative, <0
substitute each tst point into the function and consider its