timcrewgreen
New member
- Joined
- Jul 30, 2013
- Messages
- 2
Hello all, I'm new around here. Just wondered if anybody could help me with some trouble I'm having. I'm trying to teach myself English Maths A Level inside a year to progress in my career. I'm now 29 so it has been 13 years since I was taught Maths (that's plural
) in a classroom setting, so I am rather rusty. I have a reasonable grasp of the basics but consistently find myself unable to work out the more complicated questions. I've only covered Surds and algebra in my studies so far. There must be something slightly off about the way I'm approaching problems for me to be having these consistent difficulties, but without tutorial guidance I'm unable to figure out what this must be. I thought it would be a good idea to post an example here to demonstrate what I mean. If somebody shows me where I am going wrong in this very specific example maybe it will help me going forward.
I'm currently working on the inequalties section of my course book. I am stuck on the following problem (the answer is at the back of the book, obviously, but I have no idea how to get that answer)-
Find the range of values of k that give this equation no real roots (k+1)x² +4kx + 9 =0
Ok, I figure this is a problem where I have to consider the discriminant. So a = (k+1) b = 4k and c = 9
This makes the full discriminant the following - 4k² - 4 x (k+1) x 9.
By multiplying out the brackets I'm getting this - 4k² - 36k - 36. So this is becomes a quadratic equation. To me it looks like you can't factorise, so instead I opt to complete the square. So when p = the coefficient of the k² term, q = to the coefficient of the k term, and r = the coefficient of the constant term, p = 4. Therefore, I'm assuming that -36 = 2pq, or in other words 2 x 4 x q. So -36 = 8q. This would make q = -4½. I also assume -36 = pq² + r, or 4 x (-4½)² + r. Therefore -36 = 81 + r. Therefore r = -117.
The full expression of the completed square according to all the above assumptions is 4(k - 4½)² - 117. This would mean 4(k - 4½)² = 117. Which would then mean (k - 4½)² = 117/4 = 29¼. Then (k - 4½) = √29¼ which as far as I can see can't be simplified into an integer or a surd. I could express it as the √(117/4), which is equal to the √117/2. The square root of 117 can be expressed as the square root of (13 x 9), which would give you k - 4½ = (3√13)/2
The above assumptions mean k = 4½ ± (3√13)/2. However, the answer is apparently -¾ < k < 3. I understand that the k that I found is only supposed to apply when the left side of the discriminant is = to the right hand side, which would when the equation would have equal roots, and in fact I need to find a range of values that means the right hand side of the discriminant is higher therefore there are no real roots. I just can't understand how you would get that range of values, I'm obviously doing something wrong, can somebody please help? Cheers
) in a classroom setting, so I am rather rusty. I have a reasonable grasp of the basics but consistently find myself unable to work out the more complicated questions. I've only covered Surds and algebra in my studies so far. There must be something slightly off about the way I'm approaching problems for me to be having these consistent difficulties, but without tutorial guidance I'm unable to figure out what this must be. I thought it would be a good idea to post an example here to demonstrate what I mean. If somebody shows me where I am going wrong in this very specific example maybe it will help me going forward.I'm currently working on the inequalties section of my course book. I am stuck on the following problem (the answer is at the back of the book, obviously, but I have no idea how to get that answer)-
Find the range of values of k that give this equation no real roots (k+1)x² +4kx + 9 =0
Ok, I figure this is a problem where I have to consider the discriminant. So a = (k+1) b = 4k and c = 9
This makes the full discriminant the following - 4k² - 4 x (k+1) x 9.
By multiplying out the brackets I'm getting this - 4k² - 36k - 36. So this is becomes a quadratic equation. To me it looks like you can't factorise, so instead I opt to complete the square. So when p = the coefficient of the k² term, q = to the coefficient of the k term, and r = the coefficient of the constant term, p = 4. Therefore, I'm assuming that -36 = 2pq, or in other words 2 x 4 x q. So -36 = 8q. This would make q = -4½. I also assume -36 = pq² + r, or 4 x (-4½)² + r. Therefore -36 = 81 + r. Therefore r = -117.
The full expression of the completed square according to all the above assumptions is 4(k - 4½)² - 117. This would mean 4(k - 4½)² = 117. Which would then mean (k - 4½)² = 117/4 = 29¼. Then (k - 4½) = √29¼ which as far as I can see can't be simplified into an integer or a surd. I could express it as the √(117/4), which is equal to the √117/2. The square root of 117 can be expressed as the square root of (13 x 9), which would give you k - 4½ = (3√13)/2
The above assumptions mean k = 4½ ± (3√13)/2. However, the answer is apparently -¾ < k < 3. I understand that the k that I found is only supposed to apply when the left side of the discriminant is = to the right hand side, which would when the equation would have equal roots, and in fact I need to find a range of values that means the right hand side of the discriminant is higher therefore there are no real roots. I just can't understand how you would get that range of values, I'm obviously doing something wrong, can somebody please help? Cheers
