Which one of the following equations has no real solutions?
Tick (✓) one box - AQA - A-Level Maths Pure - Question 2 - 2020 - Paper 2
Question 2
Which one of the following equations has no real solutions?
Tick (✓) one box.
- cot.x = 0
- ln.x = 0
- |x + 1| = 0
- sec.x = 0
Worked Solution & Example Answer:Which one of the following equations has no real solutions?
Tick (✓) one box - AQA - A-Level Maths Pure - Question 2 - 2020 - Paper 2
Step 1
cot.x = 0
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Answer
The equation cot.x = 0 implies that x = (2n + 1) rac{ ext{π}}{2}, where n is an integer. Thus, this equation has real solutions.
Step 2
ln.x = 0
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Answer
The equation ln.x = 0 implies that x = 1, which is a real solution. Therefore, this equation has real solutions.
Step 3
|x + 1| = 0
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Answer
The equation |x + 1| = 0 implies that x + 1 = 0, leading to x = -1. This equation has a real solution.
Step 4
sec.x = 0
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Answer
The secant function sec.x = rac{1}{ ext{cos.x}} has no solutions when cos.x = 0. Therefore, the equation sec.x = 0 has no real solutions.
