Math, asked by chinna6859294, 6 months ago

1) find the value of 'k' for which the equation x^2+2(k+1) x+k^2=0 has equal roots

Answers

Answered by k047

$\huge \bf \underline\pink{FoRmuLa:}$

Let any given quadratic equation be

ax² + bx + c = 0 ..... (1)

For equal roots, we have

discriminant = 0

i.e., b² - 4ac = 0

$\huge \bf \underline \purple{ ExpLanaTioN}$

The given equation is

x² + 2 (k + 1)x + k² = 0

Comparing with equation (1), we get

a = 1, b = 2 (k + 1), c = k²

For equal roots,

b² - 4ac = 0

or, {2 (k + 1)}² - 4 * 1 * k² = 0

or, 4 (k² + 2k + 1) - 4k² = 0

or, 4k² + 4 (2k + 1) - 4k² = 0

or, 4 (2k + 1) = 0

or, 2k + 1 = 0

or, 2k = - 1

or, k = - 1/2

Therefore, the value of k is (- 1/2)

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