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11 Nov 2012, 11:28
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
71% (01:38) correct
29%
(02:07)
wrong
based on 40
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The equation Ax + By + C = 0 represents a family of straight lines passing through a fixed point M. If 2 and – 3 are two of the three roots of the equation Ax3 + Bx2 + Cx + D = 0, then what are the co – ordinates of the point M
a. (6, - 1)
b. (5, - 2)
c. (7, 1)
d. (7, - 1)
e. (6, 1)
a. (6, - 1)
b. (5, - 2)
c. (7, 1)
d. (7, - 1)
e. (6, 1)
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11 Nov 2012, 21:49
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kingb
Two roots are given, thus they should satisfy the given equation. Substituting values of roots 2 and -3 in equation Ax3 + Bx2 + Cx + D = 0
we get:
8A+4B+2C+D =0
and
-27A+9B-3C+D=0
Substract these two equations:
35A-5B+5C =0
or
7A-B+C=0
However this represents the line of family:
Ax + By + C = 0
The coordiante of point M satisfy this equation as well. Comparing these two statemetns quickly we can come up with point:
x=7, y=-1
Ans D it is!
PS: Also, please always provide OA.
seriousmonkey
11 Nov 2012, 22:26
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It should be D.
We can substitute the two roots and get a relation between A,B and C as Vips0000 has done. We can then choose the answer from the options to fit the questions.
As an aside, we can also solve for A,B and C. Just consider that -B/A is the sum of the roots, where the roots are 2,-3,k and C/A the sum of the product of the roots taken two at a time. We can divide 7A= B+C by A on both sides and solve for the third root.
B/A + C/A =7
-(-B/A)+C/A=7
-(2-3+k) + (2*-3 +2*k -3*k) = 7
Substituting the values, we should get the third root as -6.
We can substitute this in the equation form (x-2)(x+3)(x-k) where k=-6 and we can get A=1, B=8 and C=1. The line is x+8y+1=0 and again, it passes only (7,-1).
Again, vips0000 has the fastest solution. This is just one way to solve for other parameters, if they are asked in a similar question.
We can substitute the two roots and get a relation between A,B and C as Vips0000 has done. We can then choose the answer from the options to fit the questions.
As an aside, we can also solve for A,B and C. Just consider that -B/A is the sum of the roots, where the roots are 2,-3,k and C/A the sum of the product of the roots taken two at a time. We can divide 7A= B+C by A on both sides and solve for the third root.
B/A + C/A =7
-(-B/A)+C/A=7
-(2-3+k) + (2*-3 +2*k -3*k) = 7
Substituting the values, we should get the third root as -6.
We can substitute this in the equation form (x-2)(x+3)(x-k) where k=-6 and we can get A=1, B=8 and C=1. The line is x+8y+1=0 and again, it passes only (7,-1).
Again, vips0000 has the fastest solution. This is just one way to solve for other parameters, if they are asked in a similar question.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
