Question

For what values of k, the given equations have real and equal roots? (i) x^2 – 2(k + 1)x + k^2 = 0 (ii) k^2x^2 – 2(2k-1)x + 4 = 0​

Answer 1

Answer:

k

2

x

2

−2(2k−1)x+4=0

⇒ Here, a=k

2

,b=−2(2k−1),c=4

⇒ It is given that roots are real and equal.

∴ b

2

−4ac=0

⇒ [2(2k−1)]

2

−4(k

2

)(4)=0

⇒ 4(4k

2

−4k+1)−16k

2

=0

⇒ 16k

2

−16k+4−16k

2

=0

⇒ −16k=−4

∴ k=

4

1

∴ We can see value of k given in question is correct.

Step-by-step explanation:

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Answer 2

formulae for finding roots is b^2 -4ac