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Simple Maths Question, Please help?
4. (a) Simplify completely .
(2x^2 - 7x + 3 / x^2 - x - 6) - 1
(b) Hence or otherwise, find the value of the expression when x = 0.5.
5) It is given that -1/2 is a root of the equation 10n^2-9n+k = 0 , where k is a constant. Find
(a) the value of k
(b) the other root
2 Answers
- NoneLv 79 years ago
(a) (2x^2 - 7x + 3)/(x^2 - x - 6) - 1 =
[(2x - 1)(x -3)/(x + 2)(x - 3)] - 1 =
(2x - 1)/(x + 2) - 1 =
(2x - 1 - x - 2)/(x + 2) =
(x - 3)/(x + 2) =
-2.5/2.5 = - 1 when x = 0.5
10n^2 - 9n + k = 0; n = - 1/2
5/2 + 9/2 =14/2 = -k
k = -7
10n^2 - 9n - 7 = (2n + 1)(5n - 7)
n = 7/5, - 1/2
- Anonymous9 years ago
a) ((2x^2-7x+3)/(x^2-x-6))-1=((2x-1)(x-3)/(x+2)(x-3))-1=(2x-1/x+2)-1=x-3/x+2
b) substitute x=0.5 in the solution of a we get 0.5-3/0.5+2= -2.5/2.5=-1
5) as one of root is given as -1/2 it should ssatisfy the eq.
substitute n=-1/2 in given eq.
=> 10(1/4)-9(-1/2)+k=0
=>5/2+9/2+k=0
=>14/2+k=0
=>k=-7
now to find other root of eq. 10n^2-9n-7=0
=>10n^2-14n+5n-7=0
=>2n(5n-7)+1(5n-7)=0
=>(2n+1)(5n-7)=0
=>n=-1/2&n=7/5
therefore the other root iis 7/5.. :)
