How do you solve the inequality x^2-6x-7<0

tearstreakdl 2021-12-15 Answered
How do you solve the inequality x26x7<0
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Expert Answer

Elaine Verrett
Answered 2021-12-16 Author has 41 answers
Explanation:
First, factorise the x terms.
x26x7<0
(x7)(x+1)<0
To find the roots:
x7=0 or x+1=0
x=7 or x=1
The question asks us to find the portion of the curve which is less than zero (<0). Thus, we need to show by giving a range of values of x.
Do a rough sketch of a graph showing
x2 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 y=0
This means the curve is negative between x=1 and x=7
Which is expressed as 1<x<7
(If the question states x26x7>0, the portions of the curve that are positive is when x<1 and x>7)
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Jenny Bolton
Answered 2021-12-17 Author has 32 answers
Explanation the quadratic on the left side
(x7)(x+1)<0
find the zeros
x=1 and x=7
These indicate where the function changes sign
the zeros split the x-axis into 3 intervals
x<1, 1<x<7, x>7
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
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