Maths help (quadratic inequalities)Watch
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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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?
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.
- Visualise or draw the graph
- 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 , obvioulsy the solutions would be 2 and -2, so plug into the initial equation and you get out the sultion , this would satisfy the inequality so the solution would be
If the inequality were you would follow the same procedure, except would not satisfy the inequality, so the solution would be (the or being important)