If the equation x^2-2x(1+3k)+7(3+2k)=0 has eqaul roots, then find the

1.	If the equation x^2-2x(1+3k)+7(3+2k)=0 has eqaul roots, then find the valur of k.
Answer» Given, x2 - 2x(1 + 3k) + 7(3 + 2k) = 0Here, a = 1, b = -2(1 + 3k) and c = 7(3 + 2k)The given equation will have equal roots, ifD = 0{tex}\\Rightarrow{/tex}\xa0b2\xa0- 4ac = 0\xa0{tex}\\Rightarrow{/tex}4(1 + 3k)2 - 4\xa0{tex}\\times{/tex} 1\xa0{tex}\\times{/tex} 7(3 + 2k)\xa0= 0{tex} \\Rightarrow{/tex}4(3k\xa0+ 1)2 - 4\xa0{tex}\\times{/tex} 1\xa0{tex}\\times{/tex} 7(3 + 2k) = 0{tex}\\Rightarrow{/tex}\xa04(9k2\xa0+ 1 +6k) - 4(21 + 14k) = 0{tex}\\Rightarrow{/tex}\xa04(9k2\xa0+1 +6k) - 84 - 56k = 0{tex}\\Rightarrow 36k^2+4+24k-84-56k=0 {/tex}{tex} \\Rightarrow{/tex}\xa04(9k2 - 8k- 20) = 0{tex} \\Rightarrow{/tex}\xa09k2 - 8k -20 = 0{tex} \\Rightarrow{/tex}\xa09k2 - 18k + 10k\xa0- 20 = 0{tex} \\Rightarrow \\quad ( k - 2 ) ( 9 k + 10 ) = 0 \\Rightarrow k - 2 = 0 \\text { or, } 9 k + 10 = 0 \\Rightarrow k = 2 \\text { or, } k = - \\frac { 10 } { 9 }{/tex}

If the equation x^2-2x(1+3k)+7(3+2k)=0 has eqaul roots, then find the valur of k.