Maths help (quadratic inequalities)

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Excuse Me!
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Hi, can someone have a look at questions 44-49 for me. I have attached my answers (and method) for 44-47 but am not sure about them.

Q 48-49 I would appreciate someone helping me to start as I am not sure how the quadratic formulae comes into use

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HandmadeTurnip
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Can you upload bigger pictures? It's impossible to read them.
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Excuse Me!
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(Original post by HandmadeTurnip)
Can you upload bigger pictures? It's impossible to read them.
Are they better?


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cuckoo99
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it helps to draw graphs when solving quadratic inequality's if you are having problems with which way the inequality sign faces,
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HandmadeTurnip
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(Original post by Excuse Me!)
Are they better?


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Yes, that's better.

44. Correct

45. You've factorized correctly but think about what the graph would look like. The question's asking you where it would be positive, i.e. above the X-axis.

46. The second root should be -1/3, which means you'll need to change your answer around a bit.

47. Again, you've factorized correctly but your answer's wrong. If a quadratic has repeated roots what does that mean? and what implications does that have for what the graph looks like?
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cuckoo99
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Ok i understand what ur asking now , ok

48.
you are gunna need to use the quadratic formula to find the critical values of the inequality. Then look at the inequality and draw it. shade in the area that satisfys the inequality , and then form the inequality expression(s) accordingly. Its kinda hard to explain more without just showing you all the working.
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HandmadeTurnip
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For questions 48 and 49, you can't factorize them so you need to plug them into the quadratic formula to find their roots.
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Jammy Duel
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Solve them as if they were just equations (using the quadratic formula since it hinted that), then work out which way around the inequalities should be, there are a few ways:
  1. Visualise or draw the graph
  2. Consider points either side of the values found

The first is going to be easier since the graphs won't be too hard to plot, the second is probably a bit quicker if you can't visualise the graph. If you pick an arbitrary point between your values of x (preferably one that's easy to get the answer for, so 0 if possible). If that point satisfies the inequality in the question then put the signs so as to make that value part of the solution set; if that point doesn't satisfy the question inequality then set your answer inequalities to not include that point.

eg: suppose it was asking for the solutions to x^2-4\leq0, obvioulsy the solutions would be 2 and -2, so plug x=0 into the initial equation and you get out the sultion -4, this would satisfy the inequality so the solution would be -2\leq x\leq2
If the inequality were x^2-4\geq0 you would follow the same procedure, except x=0 would not satisfy the inequality, so the solution would be x\leq-2 or x\geq2 (the or being important)
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(Original post by Excuse Me!)
Hi, can someone have a look at questions 44-49 for me. I have attached my answers (and method) for 44-47 but am not sure about them.

Q 48-49 I would appreciate someone helping me to start as I am not sure how the quadratic formulae comes into use

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There are some notes here on quadratic inequalities if they are of any use to you http://www.mathsbridge.co.uk/2014/09...-revision.html
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