Find the value of k for which the equation 7x2+2kx+7=0 have real roots
Answers
Answered by
0
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, ∞ ).
Similar questions