Question

Find k for which the following quadratic equation has equal roots x^2-2x(1+3k)+7(3+2k)=0

Answer 1

Answer:

k=2 or k =-10/9

Step-by-step explanation:

hope it helps

Answer 2

Answer:

• k = -10/9 and 2.

Step-by-step explanation:

Given:

• Quadratic equation x² - 2x(1 + 3k) + 7(3 + 2k) = 0 is has equal roots.

To find:

• Value of k.

Now, we know that equation has equal roots when b² - 4ac = 0.

Now, compare the given equation with, ax² + by + c = 0 to find a, b and c.

From comparing we get,

• a = 1
• b = -2(1 + 3k)
• c = 7(3 + 2k)

Now, put the values in b² - 4ac = 0

⇒ [-2(1 + 3k)]² - 4 × 1 × [7(3 + 2k)] = 0

⇒ 4(1 + 3k)² - 4 × 7(3 + 2k) = 0

⇒ 4(1 + 9k² + 6k) - 4(21 + 14k) = 0

⇒ (1 + 9k² + 6k) - (21 + 14k) = 0

⇒ 1 + 9k² + 6k - 21 - 14k = 0

⇒ 9k² - 8k - 20 = 0

Now, we will solve this equation by splitting middle term method.

⇒ 9k² - 8k - 20 = 0

⇒ 9k² - 18k + 10k - 20 = 0

⇒ 9k(k - 2) + 10(k - 2) = 0

⇒ (9k + 10)(k - 2) = 0

⇒ 9k = -10

⇒ k = -10/9

⇒ k - 2 = 0

⇒ k = 2

Hence, k = -10/9 and 2.

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