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find the non zero value of k , which the quadratic equation kx^2 + 1 - 2 (k-1) x+x^2 = 0 has equal roots . hence find the roots of the equation .
please fast ⏩⏩
find the non zero value of k , which the quadratic equation kx^2 + 1 - 2 (k-1) x+x^2 = 0 has equal roots . hence find the roots of the equation .
please fast ⏩⏩
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Verified answer
Step-by-step explanation:
kx^2 + 1 - 2 (k-1) x+x^2 =0
kx^2 + x^2 + 1+(- 2k +2)x = 0
(k + 1)x^2 +(-2k + 2)x + 1 = 0
here , a = (k+1) , b = (-2k + 2) and c = 1
b² - 4ac = 0 (for equal roots)
(-2k + 2)² - 4 x (k+1) x 1 = 0
4k² -8k + 4 - 4k - 4 = 0
4k² - 12k = 0
4k(k - 3) = 0
k = 0 or 3
hence , k = 3