The integral value of k for which the equation (k−12)x2+2(k−12)x+2=0 possesses no real solutions is :
A
12
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B
13
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C
14
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D
15
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Solution
The correct option is B 13 We have (k−12)x2+2(k−12)x+2=0 For no real solution, D < 0 i.e b2−4ac<0 ⇒[2(k−12)]2−4(k−12)×2<0 ⇒2(k−12)[2(k−12)−4]<0 ⇒(k−12)[2k−24−4]<0 ⇒(k−12)(2k−28)<0 ⇒12<k<14 ⇒k=13