# In each of the following determine the; value of k for which the given value is a solution of the equation:

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In each of the following determine the; value of k for which the given value is a solution of the equation:

(i) Since, x = 2 is a root of the given equation, therefore, it satisfies the equation  i.e.,

k(2)2 + 2 × 2 -3 = 0

⇒ 4k + 1 = 0 ⇒ k = - ¼

(ii) Since, x = -1/2 is a root of the given equation

3x2 + 2kx – 3 = 0

Therefore,

3(-1/2)2 + 2k(-1/2) - 3 = 0

⇒ 3 × ¼  -  k – 3 = 0

⇒ k = ¾ - 3 = - 9/4

⇒ k = - 9/4

(iii) Since, x = - a is a root of the equation

x2 + 2ax – k = 0

⇒ (- a)2 + 2a × (- a) – k = 0

⇒ a2 – 2a2 – k = 0

⇒  - k = a2 ⇒ k = - a2