InterviewSolution
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InterviewSolution
| 1. |
9x2-9(p+q)x+(2p2+5pq+2q2)solve this for x |
| Answer» Given{tex}9 x ^ { 2 } - 9 ( a + b ) x + 2 a ^ { 2 } + 5 a b + 2 b ^ { 2 } = 0{/tex}Now,\xa0{tex}2 a ^ { 2 } + 5 a b + 2 b ^ { 2 } = 2 a ^ { 2 } + 4 a b + a b + 2 b ^ { 2 }{/tex}{tex}= 2 a [ a + 2 b ] + b [ a + 2 b ]{/tex}= (a + 2b) (2a + b)Hence the given equation becomes,{tex}9 x ^ { 2 } - 9 ( a + b ) x + ( a + 2 b ) ( 2 a + b ) = 0{/tex}or,\xa0{tex}9 x ^ { 2 } - 3 [ 3 a + 3 b ] x + ( a + 2 b ) ( 2 a + b ) = 0{/tex}{tex}9x^2-3(a+2b)x-3(2a+b)x+(a+2b)(2a+b)=0{/tex}{tex}3x[3x-(a+2b)]-(2a+b)[3x-(a+2b)]=0{/tex}or,\xa0{tex}[ 3 x - ( a + 2 b ) ] [ 3 x - ( 2 a + b ) ] = 0{/tex}{tex}\\Rightarrow\\ either\\ 3x=a+2b\\ or\\ 3x=2a+b{/tex}{tex}\\Rightarrow\\ either\\ x=\\frac{a+2b}{3}\\ or\\ x=\\frac{2a+b}{3}{/tex}Hence, the roots =\xa0{tex}\\frac { a + 2 b } { 3 } , \\frac { 2 a + b } { 3 }{/tex} | |