Find that non zero value of …
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Sia ? 6 years, 6 months ago
we have to find that non-zero value of k, for which the quadratic equation kx2 +1 - 2(k - l)x +x{tex}^2{/tex} = 0 has equal roots.
Given, {tex}k x ^ { 2 } + 1 - 2 ( k - 1 ) x + x ^ { 2 } = 0{/tex}
{tex}( k + 1 ) x ^ { 2 } - 2 ( k - 1 ) x + 1 = 0{/tex}
For equal roots {tex}D = b ^ { 2 } - 4 a c = 0{/tex}
Here, a= k + 1,b = -2 (k -1), c = 1
{tex}4 ( k - 1 ) ^ { 2 } - 4 ( k + 1 ) \times 1 = 0{/tex}
or, {tex}4 k ^ { 2 } - 8 k + 4 - 4 k - 4 = 0{/tex}
or, {tex}4 k ^ { 2 } - 12 k = 0{/tex}
or, {tex}4 k ( k - 3 ) = 0{/tex}
{tex}\therefore {/tex} k=3 [k=0 is rejected as it is coefficient of {tex}x^2{/tex}]
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