Solve the inequality - OCR - GCSE Maths - Question 17 - 2017 - Paper 1
Question 17
Solve the inequality.
$$x^2 - 5x - 6 < 0$$
Worked Solution & Example Answer:Solve the inequality - OCR - GCSE Maths - Question 17 - 2017 - Paper 1
Step 1
Factor the quadratic expression
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Answer
To solve the inequality, we first factor the quadratic expression. We need to find two numbers that multiply to -6 and add up to -5. The numbers -6 and 1 meet these criteria.
Thus, the equation can be factored as:
(x−6)(x+1)<0
Step 2
Determine the critical points
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Answer
Setting the factors equal to zero gives the critical points:
x−6=0⇒x=6
x+1=0⇒x=−1
These points will help to identify the intervals to test.
Step 3
Test intervals
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Answer
Next, we test the intervals determined by our critical points:
For the interval (−∞,−1), choose x=−2:
(−2−6)(−2+1)=(−8)(−1)=8>0
For the interval (−1,6), choose x=0:
(0−6)(0+1)=(−6)(1)=−6<0
For the interval (6,∞), choose x=7:
(7−6)(7+1)=(1)(8)=8>0
Step 4
Write the solution
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Answer
The inequality is satisfied for the interval where the product is less than zero, which is:
−1<x<6
Thus, the final solution to the inequality is:
x∈(−1,6)
