Find out the value of k for which the expression $x^{2} + (k + 5) x - k - 5 = 0$ has two distinct real roots.

(

, -9] U [-5,

)

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(

, -9) U (-5,

)

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(

, -9) U (-3,

)

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(-9, -5)

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[-9, -5]

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Solution

The correct option is B (, -9) U (-5, )
Soln:

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

Hence option (b)

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Question 9
Which of the following equation has two distinct real roots?
(a) $2 x^{2} - 3 \sqrt{2} x + \frac{9}{4} = 0$
(b) $x^{2} + x - 5 = 0$
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Find out the value of k for which the expression x2+(k+5)x−k−5=0 has two distinct real roots.

The correct option is B (, -9) U (-5, )Soln: For the equation given D=(k+5)2+4(1)(k+5)=k2+10k+25+4k+20=k2+14k+45 For the equation to have two distinct roots: D>0 k2+14k+45>0 (k+9)(k+5)>0 Value of k will be (−∞,−9)∪(−5,∞) Hence option (b)

Find out the value of k for which the expression $x^{2} + (k + 5) x - k - 5 = 0$ has two distinct real roots.