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Find the Value of K for Which the Following Equation Has Equal Roots. X2 + 4kx + (K2 – K + 2) = 0 - ICSE Class 10 - Mathematics

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Question

Find the value of k for which the following equation has equal roots.

x2 + 4kx + (k2 – k + 2) = 0

Solution

For the given equation x2 + 4kx + (k2 – k + 2) = 0

a = 1, b = 4k and c = k2 - k +1

Since the roots are equal,

b2 - 4ac  = 0

`=> (4k)^2 - 4xx1xx(k^2 - k + 2) = 0`

`=> 16k^2 - 4k^2 + 4k - `8 = 0`

`=> 12k^2 + 4k - 8 = 0`

`=> 3k^2 + k - 2 = 0`

`=> 3k^2 + 3k - 2k - 2 = 0`

`=> 3k(k+1) - 2(k+1) = 0`

`=> (k+1) (3k - 2) = 0`

`=> k + 1 = 0 or 3k - 2 = 0`

`=> k = -1 or k = 2/3`

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Solution Find the Value of K for Which the Following Equation Has Equal Roots. X2 + 4kx + (K2 – K + 2) = 0 Concept: Nature of Roots.
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