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# Maths GCSE 9-1 Help Needed PLEASE

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1. "Write down all the integer values that satisfy the inequality x^2 - 4x ≤ 0"

Anyone has a step by step guide on how to do it?
2. It is just x ≤ 0 isn't it, x^2 -4x is a quadratic graph, and it crosses the x-axis at (0,0) and (4,0)
As the question is asking for the integers values when x^2 - 4x ≤ 0, you can either draw a graph and notice that 0 ≤ x ≤ 4 satisfy the equation, or just do it in your head.
Do I need to tell you the answers?
3. x^2 - 4x ≤ 0

So to begin with, we know that this is a quadratic (has two solutions) as it contains x^2 as the first term.
Additionally, we know that in a quadratic each of these "solutions" is actually just an x value where the result is zero.

We're looking for any results less than or equal to zero, so we want each x value between our two solutions.
We can find solutions by factorising:

(x + 0)(x - 4) - we found this by finding two numbers which multiply to give zero and add to give -4.

As a result, we can find the solutions, as we know that for the result to be zero one of the two brackets must equal zero (to times with the other to give zero):

x + 0 = 0 (so x is zero)
x - 4 = 0 (so x is four)

So, we want all of the numbers between zero and four, and this INCLUDES zero and four because of the "or equal" inequality sign. We also only want integers as stated in the question, so the answer is zero, one, two, three and four.

Hope this helps :-)
4. (Original post by console.log)
x^2 - 4x ≤ 0

so to begin with, we know that this is a quadratic (has two solutions) as it contains x^2 as the first term.
Additionally, we know that in a quadratic each of these "solutions" is actually just an x value where the result is zero.

We're looking for any results less than or equal to zero, so we want each x value between our two solutions.
We can find solutions by factorising:

(x + 0)(x - 4) - we found this by finding two numbers which multiply to give zero and add to give -4.

As a result, we can find the solutions, as we know that for the result to be zero one of the two brackets must equal zero (to times with the other to give zero):

X + 0 = 0 (so x is zero)
x - 4 = 0 (so x is four)

so, we want all of the numbers between zero and four, and this includes zero and four because of the "or equal" inequality sign. We also only want integers as stated in the question, so the answer is zero, one, two, three and four.

Hope this helps :-)

brilliant thanks mate!

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