Find out the value of k for which the expression x2+(k+5)x−k−5=0 has two d

Question

Find out the value of k for which the expression

x^{2} + (k + 5) x - k - 5 = 0

has two distinct real roots.

Options:

A . (−∞,−9]∪[−5,∞)

B . (−∞,−9)∪(−5,∞)

C . (−∞,−9)∪(−3,∞)

D . (-9, -5)

Answer: Option B
:
B
For the equation given

D = (k + 5)^{2} + 4 (1) (k + 5) = k^{2} + 10 k + 25 + 4 k + 20 = k^{2} + 14 k + 45

For the equation to have two distinct roots:

D > 0

k^{2} + 14 k + 45 > 0 (k + 9) (k + 5) > 0

Value of k will be

(- \infty, - 9) \cup (- 5, \infty)

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