Find the values of k for which the following equation has equal roots:
x² - 2kx + 7k - 12 = 0

Question

Find the values of k for which the following equation has equal roots: x2 - 2kx + 7k - 12 = 0

KnowledgeBoat · Accepted Answer

Comparing x2 - 2kx + 7k - 12 = 0 with ax2 + bx + c = 0 we get, a = 1, b = -2k and c = (7k - 12). Since equations has equal roots, ∴ D = 0 ⇒ (-2k)2 - 4 × 1 × (7k - 12) = 0 ⇒ 4k2 - (28k - 48) = 0 ⇒ 4k2 - 28k + 48 = 0 ⇒ 4k2 - 16k - 12k + 48 = 0 ⇒ 4k(k - 4) - 12(k - 4) = 0 ⇒ (k - 4)(4k - 12) = 0 ⇒ (k - 4) = 0 or (4k - 12) = 0 [Using Zero-product rule] ⇒ k = 4 or 4k = 12 ⇒ k = 4 or k = ⇒ k = 4 or k = 3. Hence, k = {4, 3}.

Mathematics

Find the values of k for which the following equation has equal roots:
x² - 2kx + 7k - 12 = 0

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Mathematics

Find the values of k for which the following equation has equal roots:x2 - 2kx + 7k - 12 = 0

Quadratic Equations

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