The equations k x 2 + x + k = 0 and k x 2 + k x + 1 = 0 have exactly one root in common for

Step-by-step solution

Let α be the common root ⇒ k α 2 + α + k = 0 k α 2 + k α + 1 = 0 On solving, we get, α 2 1 - k 2 = α k 2 - k = 1 k 2 - k α 2 α = 1 - k 2 k 2 - k and α 1 = k 2 - k k 2 - k ⇒ α = 1 - k 2 k 2 - k = 1 ⇒ k 2 - k = 1 - k 2 ⇒ 2 k 2 - k - 1 = 0 ⇒ k = - 1 2 , 1 For k = 1 , equations are identical, thus not possible Hence, k = - 1 2