Write the condition for the roots of the equation (a2+b2)x2 -2b(a+c)x + (b2+c2)=0 to be equal

Write the condition for the roots of the equation (a2+b2)x2 -2b(a+c)x

1.	Write the condition for the roots of the equation (a2+b2)x2 -2b(a+c)x + (b2+c2)=0 to be equal
Answer» We have the following equation,{tex}(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0{/tex}Since equation\xa0has\xa0equal roots,D = 0{tex}\\Rightarrow{/tex}\xa0B2\xa0- 4AC\xa0= 0{tex}\\Rightarrow{/tex}\xa0[-(2ab + 2bc)]2\xa0- 4(a2 + b2)(b2 +c2) = 0{tex}\\Rightarrow{/tex}\xa0[4a2b2\xa0+ 4b2c2\xa0+ 8ab2c] - 4[a2b2\xa0+ a2c2\xa0+ b4\xa0+ b2c2] = 0{tex}\\Rightarrow{/tex}\xa0[4a2b2\xa0+ 4b2c2\xa0+ 8ab2c] -4a2b2\xa0-4a2c2\xa0-4b4\xa0- 4b2c2 = 0{tex}\\Rightarrow{/tex}\xa0-4b4\xa0-4a2c2\xa0+ 8ab2c = 0\xa0{tex}\\Rightarrow{/tex}\xa0-4(b4\xa0+\xa0a2c2\xa0-2ab2c) = 0{tex}\\Rightarrow{/tex}\xa0b4\xa0+ a2c2\xa0- 2ab2c = 0\xa0{tex}\\Rightarrow{/tex}\xa0(b2\xa0- ac)2\xa0= 0\xa0{tex}\\Rightarrow{/tex}\xa0b2\xa0- ac = 0\xa0{tex}\\Rightarrow{/tex}\xa0b2 = ac