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# C1 - How do I find the set of possible values of K - 5k^2 - 12k <0 watch

1. Question is this:

The equation kx^2 + kx + 3-k =0, where k is a constant, has no real roots.
a) Show that 5k^2 - 12k <0 (I have done this, I understand that)
b) Find the set of possible values of k (4 marks)

I don't have a clue how to do part B. Please could you help me and explain it to me?
2. (Original post by blobbybill)
Question is this:

The equation kx^2 + kx + 3-k =0, where k is a constant, has no real roots.
a) Show that 5k^2 - 12k <0 (I have done this, I understand that)
b) Find the set of possible values of k (4 marks)

I don't have a clue how to do part B. Please could you help me and explain it to me?
Try sketching a graph
3. Factorise.
You have k(5k - 12) < 0.
remember to get a negative when you multiply two numbers together, the numbers must have different signs.
4. (Original post by 13 1 20 8 42)
Factorise.
You have k(5k - 12) < 0.
remember to get a negative when you multiply two numbers together, the numbers must have different signs.
So I would factorise it, getting k=0 and k=12/5. However, the answer is 0<k<2.4

How on earth do you get that answer?
5. (Original post by blobbybill)
So I would factorise it, getting k=0 and k=12/5. However, the answer is 0<k<2.4

How on earth do you get that answer?
You've solved the equality. This is an inequality. But yes the same critical values are important; btw 2.4 = 12/5.
The point is that if you want the whole expression to be negative the two factors have to have different signs. Positive*negative = negative, negative*positive = negative while positive*positive = positive, negative*negative = negative.
So this can happen in one of two ways: k < 0 and 5k-12 > 0 or k > 0 and 5k-12 < 0
Can you take it from there?

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