The values of k for which the quadratic equation 9x2 - 3kx + k = 0, has equal roots, are: 1. 0, 1 2. 0, 2 3. 2, 4 4. 0, 4

Comparing 9x2 - 3kx + k = 0 with ax2 + bx + c = 0 we get, a = 9, b = -3k and c = k. We know that, Since equations has equal roots, ⇒ D = 0 ⇒ b2 - 4ac = 0 ⇒ (-3k)2 - 4(9)(k) = 0 ⇒ 9k2 - 36k = 0 ⇒ 9k(k - 4) = 0 ⇒ 9k = 0 or (k - 4) = 0 [Using Zero-product rule] ⇒ k = 0 or k = 4. Hence, option 4 is the correct option.

Mathematics

The values of k for which the quadratic equation 9x² - 3kx + k = 0, has equal roots, are:
0, 1
0, 2
2, 4
0, 4

Quadratic Equations

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Answer

Comparing 9x² - 3kx + k = 0 with ax² + bx + c = 0 we get,

a = 9, b = -3k and c = k.

We know that,

Since equations has equal roots,

⇒ D = 0

⇒ b² - 4ac = 0

⇒ (-3k)² - 4(9)(k) = 0

⇒ 9k² - 36k = 0

⇒ 9k(k - 4) = 0

⇒ 9k = 0 or (k - 4) = 0 [Using Zero-product rule]

⇒ k = 0 or k = 4.

Hence, option 4 is the correct option.

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Mathematics

The values of k for which the quadratic equation 9x² - 3kx + k = 0, has equal roots, are:
0, 1
0, 2
2, 4
0, 4

Quadratic Equations

Answer

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