Question

The set of values of k for which the exactly one root of the equation x2 + 2kx - 1 = 0 lie in the interval (1, 3) is​

Answer 1

Answer:

8

Step-by-step explanation:

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MATHS

Number of integral values of k for which exactly one root of the equation 5x

2

+(k+1)x+k=0 lies in the interval (1,3) is

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ANSWER

According to the question,

if,f(x)=5x

2

+(k+1)x+k=0

f(1)<0

⇒5+k+1+k<0

⇒6+2k<0

∴k<−3

andf(3)>0,

⇒5(3)

2

+(k+1)3+k>0

⇒45+3k+3+k>0

⇒48+4k>0

∴k>−12

Now,k=−12<k<−3

Valueofk=−11,−10,−9,−8,−7,−6,−5,−4

So, that the No. of integral value of k=8.