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Algebra

How am I supposed to solve question 8? I tried, but couldn`t get to the answer. I`ve attached an image, it`s question 8. Please help me out. Thanks

Question image for How am I supposed to solve question 8? I tried, bu
Profile image of Abhishek Pradhan
8 Years agoGrade
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2 Answers

Profile image of Arun
8 Years ago
Suppose new roots are p and q.
Hence
\alpha + \beta -2  = p+q
 
p+q = (-b - 2a)/a
 
\alpha-1 *\beta-1 = \alpha\beta- (\alpha + \beta) +1 = pq
 
pq = c/a + b/a +1 = (a+b+c) /a
Now
New equation will be
ax² + (b+ 2a) x + (a+b+c) = 0
Hence
a = 2
b +2a = 8
b = 4
a+b+c = 8
c = 2
Hence previous equation should be 2x² +4x + 2 = 0
Profile image of Abhishek Pradhan
8 Years ago
Thanks. As I said, I tried solving this question. And I did get to this point, when a, b & c came out to be 2, 4, and 2 respectively. But it doesn`t matches the answer at the back of the book. The answer is a/1 = b/2 = c/(-1)