Question

Find the value of k for which the equation 7x2+2kx+7=0 have real roots
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Answer 1

Answer:

The solution set of values of k is

k ∈ ( - ∞, - 7 ] ∪ [ 7, ∞ ).

Step-by-step-explanation:

The given quadratic equation is

7x² + 2kx + 7 = 0.

Comparing with ax² + bx + c = 0, we get,

• a = 7
• b = 2k
• c = 7

For real roots,

b² - 4ac ≥ 0

⇒ ( 2k )² - 4 * 7 * 7 ≥ 0

⇒ 4k² - 28 * 7 ≥ 0

⇒ 4k² - 196 ≥ 0

⇒ 4k² ≥ 196

⇒ k² ≥ 196 / 4

⇒ k² ≥ 49

⇒ k ≥ ± √49

⇒ k ≥ ± √( 7 * 7 )

⇒ k ≥ ± 7

⇒ k ≥ 7 OR k ≤ - 7

∴ The solution set of values of k is

k ∈ ( - ∞, - 7 ] ∪ [ 7, ∞ ).