Question

The value of k for which the equation x² + 2( k + 1)x + k² = 0 has equal roots is​

Answer 1

$\huge\mathfrak\green{ Question }$

ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴋ ғᴏʀ ᴡʜɪᴄʜ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ x² + 2( ᴋ + 1)x + ᴋ² = 0 ʜᴀs ᴇǫᴜᴀʟ ʀᴏᴏᴛs ɪs

$\huge\mathfrak\green{Answer}$

ᴛᴏ ʜᴀᴠᴇ ʀᴇᴀʟ ᴇǫᴜᴀʟ ʀᴏᴏᴛs,

ᴅ=0

ʙ²-4ᴀᴄ=0

ʜᴇʀᴇ ᴀ=1 ʙ=-2(ᴋ+1) ᴄ=ᴋ²

[-2(ᴋ+1)]²- 4(1)(ᴋ²)=0

[4(ᴋ²+1+2ᴋ)]-4ᴋ²=0

4ᴋ²+4+8ᴋ-4ᴋ²=0

4+8ᴋ=0

8ᴋ=-4

ᴋ= $\frac{-1}{2}$

Answer 2

Answer:

${x}^{2} + 2(k + 1)x + {k}^{2} = 0$

if roots are equal then D=b^2-4ac=0

D=(2(k+1))^2-4 (1)(k^2)=0

=>(2k+2)^2-4k^2=0

4k^2+8k+4-4k^2=0

8k+4=0

8k=-4

k=-1/2

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