Question

3. Find the values of k for each of the following quadratic equations, so that they have real roots
please solve it. it's urgent​

Answer 1

Answer:

Step-by-step explanation:

ax² + bx + c = 0

If D = b² - 4ac ≥ 0, then quadratic equation has roots in set of the real numbers.

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(vi). (k + 1)x² + 2(k + 3)x + (k + 8) = 0

D = 2²(k + 3)² - 4(k + 1)(k + 8)

2²(k + 3)² - 4(k + 1)(k + 8) ≥ 0

4k² + 24k  + 36 - 4k² - 36k - 32 ≥ 0

- 12k + 4 ≥ 0

3k ≤ 1

k ≤ $\frac{1}{3}$ and k ≠ - 1

For k ∈ ( - ∞, - 1 ) ∪ ( - 1, $\frac{1}{3}$ ) given quadratic equation has real roots.

(3).

(i). 2x² - 5x - k = 0

D = ( - 5)² - 4(2)( - k )

25 + 8k ≥ 0

k ≥ - $\frac{25}{8}$

For k ∈ [ - $\frac{25}{8}$, ∞ ) given quadratic equation has real roots.

(ii). 36 - 4k ≥ 0 ⇒ k ≤ 9

Now is your turn. You can do it!!!!!

Answer 2

Answer:

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Step-by-step explanation:

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