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secondary 4 | A Maths
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Hello, I would like to enquire about how to solve these types of questions that state “always positive” “2 distinct points” “always negative” etc. I always manage to solve all the way till the end but then my range of x is always wrong, and I can’t visualise how to determine the range? Eg. I have m^2 > 3, they ask for range of m that is always positive, how do I determine that range? Thank you so much in advance.
Date Posted: 3 years ago
Views: 183
The range can be determined easily by checking for it's discriminant. discriminant = b^2 - 4ac. You must use this regardless of whether the question state "always positive/negative", " 2 equal roots" and "2 distinct roots".
I'll show you the curve you expected to see for the 3 conditions.
In your example, m^2 > 3, did you use the discriminant test? If so, you are correct. Square root both sides. Then, you can find the range of m from there.
Okay, so I have m^2 > 3, square rooted both sides to get m> +- sqr root 3.
But the given answer was m > sqr root 3 only, I don’t get why the negative square root was rejected
But the given answer was m > sqr root 3 only, I don’t get why the negative square root was rejected
Can you show me the qn you get this example?
It’s q6 in this picture!
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The corresponding curve for each of the conditions.
Date Posted:
3 years ago
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Yes. It has 2 ranges. This only fulfills the "always positive and negative" condition only. Your function is either always positive or negative or even both. The question seeks for the "always positive" condition. In order to fulfill the condition fully, you need to reject the negative sqrt 3 range. This is because your x^2 coefficient is negative when you sub any values for that range. Meaning, your function is always negative. You don't have to reject only if the question states "always positive or always negative or both". I hope that answers your qn.
Date Posted:
3 years ago
Ohhhhh I get it now!!! Thanks!!
Sure np.
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