Find the value of for Which the quadratic equation (k -12)x^2 + 2(k - 12)x + 2 = 0 has two real equal roots
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Answer:ere, a = k – 12, b = 2 (k – 12), c = 2
∴ D = b2 – 4ac = [2(k– 12)]2
– 4(k – 12) x 2
= 4 (k – 12)2 – 8 (k– 12)
Roots are equal, if D = 0
⇒ 4 (k – 12) 2 – 8 (k – 12) = 0
⇒ 4(k – 12)(k – 12 – 2) = 0
⇒ (k – 12) (k – 14) = 0
⇒ k = 12 or 14
But k = 12 does not satisfy the eqn.
k = 14 Ans.
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