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1. Question:

find the value of k such that the quadratic function of x

is equal to zero for only one value of x
Find also, (a) th range of vaules of k for which the function possess a minimum value, (b) the range of values of k for which the value of the function never exceeds 12.5

sketch the graph of the function for and

My attempt:

let

i skip the a couple of steps ( please note it is only to save time)

i got

since we need to find the value of k when x = 0
in other for one of the root to be 0, the quadratic function has to be in the form; where c = 0

since c = 0

thus
k = 0.5

for (a)
using
complete the square

completing the square produces;

since f(x) has a minimum function a > 0, thus it has a least value of when x =
therefore if x =
then use to find k
x =
k =
sub k = -(3/4) into
since

therefore sub in into

.k > 175/4

part b

using

note the maximum value = 12.5

therefore

In the bostock book 'The core Course for A-level' The answer was k = -(1/48) , a) k > 1, b)

2. (Original post by bigmansouf)
Question:

find the value of k such that the quadratic function of x

is equal to zero for only one value of x
Find also, (a) th range of vaules of k for which the function possess a minimum value, (b) the range of values of k for which the value of the function never exceeds 12.5

sketch the graph of the function for and

Are you sure you expanded the square bracket correctly?
3. X doesn't equal 0. That's your mistake, I think. (This seems to have a carry on effect for the rest of the question)
I think the first part is asking for a value for k such that the equation has only one solution.

EDIT: On doing the maths on paper, this is what the question is asking for. I get k=-1/48, which matches your book
4. (Original post by an_atheist)
X doesn't equal 0. That's your mistake, I think. (This seems to have a carry on effect for the rest of the question)
I think the first part is asking for a value for k such that the equation has only one solution.

EDIT: On doing the maths on paper, this is what the question is asking for. I get k=-1/48, which matches your book
Good spot.

At first glance I interpreted the question in the same way as the OP.
5. (Original post by an_atheist)
X doesn't equal 0. That's your mistake, I think. (This seems to have a carry on effect for the rest of the question)
I think the first part is asking for a value for k such that the equation has only one solution.

EDIT: On doing the maths on paper, this is what the question is asking for. I get k=-1/48, which matches your book
thanks for correcting me
6. (Original post by notnek)

Are you sure you expanded the square bracket correctly?

im sorry but i am stuck on this question
normally to find the range of value of k you use the examples stated in Chandler's book as a guide to find it

I understand why it k > 1. We know that a quadratic function hasa a minimum value if a >0. therefore since for part a it has a minimum value for the quadratic function
rearranging the function gives

since a = k-1 and a > 0 thus k must be k> 1 in order to have minimum value

The problem is now although i understand the question and have the answer how do i write a mathematically structured answer to prove that k > 1

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