k²x²-2(k+1)x+k²=0 then find the value of k.
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The given equation is k2x2 - 2(2k - 1)x + 4 = 0
The given equation is in the form of ax2 + bx + c = 0
where a = k2, b = -2(2k - 1) and c = 4
therefore, the discriminant
D = b2 - 4ac
= (-2(2k - 1))2 - 4 x (k2) x (4)
= 4(2k - 1)2 - 16k2
= 4(4k2 + 1 - 4k) - 16k2
= 16k2 + 4 - 16k - 16k2
= 4 - 16k
∵ Roots of the given equation are real and equal
∴ D = 0
⇒ 4 - 16k = 0
⇒ -16k = -4
rARrk=-4-16
⇒ k = 1/4
Hence, the value of K = 1/4
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