Question

Find the non zero value's of k for which kx^2+1 -2(k-1)x +x^2 =0 has equal root's .
Hence find the roots.

Answer 1

Solution:

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Given:

$kx^2 + 1 -2(k-1)+x^2 =0$

$kx^2 +x^2 -2(k-1) + 1=0$

$(k+1)x^2 -2(k-1) + 1=0$ ...(i)

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To find:

The non-zero value of k,

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We know the discriminant formula that:

b² -4ac = 0 (equal roots)

(i)=> $(k+1)x^2 - 2(k-1)x + 1 = 0$

(where a= (k+1)

b = -2(k-1)

c = 1)

=> (-2(k-1))² - 4(k+1)(1) = 0

=> (4(k²-2k+1) - 4(k+1) = 0

=> 4k² - 8k + 4 -4k - 4 = 0

=> 4k² -8k -4k = 0

=> 4k² -12k = 0

=> 4k(k - 3) = 0

=> k -3 = 0

=> ∴ k = 3

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                                                         Hope it Helps !!