Question

The value of K for which the equation

2 + 2(k + 1)x + k

2 = 0 has equal roots is​

Answer 1

Step-by-step explanation:

2+2k+2×k

2+2k+2k

2+4k=0

4k=-2

k=-2/4

k=-1/2

Answer 2

AnswEr:-

Correct equation :- x² + 2(k+1)x + k².

Given:-

• x² + 2(k+1)x + k² has equal roots.

To find:-

• Value of K .

Solution:-

We know :

For any quadratic equation ax²+bx+c=0 to have equal roots , the discriminant is zero .

i.e, ❥ b² - 4ac = 0 .

Comparing given equation with ax²+bx+c  = 0 ,

➼ a=1,b=2(k+1) ,c = k²

Given that it has equal roots,

➼ b² - 4ac = 0

⇾ [2(k+1)]² - 4(1)(k²) = 0

⇾ 4k²+4(2k+1)-4k²=0

⇾ 4(2k+1)=0

⇾ 2k+1 = 0

⇾ 2k=-1

➼ k = -1/2.

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