(3k+1)x^2 + 2(k+1)x +1 find value of k which has equal roots also find

1.	(3k+1)x^2 + 2(k+1)x +1 find value of k which has equal roots also find roots
Answer» The given equation is:(3k + 1)x2 + 2(k + 1)x + 1 = 0This is of the form\xa0ax2\xa0+ bx + c = 0, wherea = 3k + 1, b = 2(k + 1) = 2k + 2 and c = 1As it is given that the given equation has real and equal roots, i.e.,\xa0D = b2\xa0- 4ac = 0.\xa0{tex}\\Rightarrow{/tex}\xa0(2k + 2)2\xa0- 4(3k + 1) (1) = 0{tex}\\Rightarrow{/tex}\xa04k2\xa0+ 8k + 4 - 12k - 4 = 0{tex}\\Rightarrow{/tex}\xa04k2\xa0- 4k = 0{tex}\\Rightarrow{/tex}\xa04k(k - 1) = 0\xa0Therefore, either 4k = 0 or k - 1 = 0{tex}\\Rightarrow{/tex}\xa0k = 0 or k = 1Hence, the roots of given equation are 1 and 0.

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