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\[kx^2-17x+2k=0\]

Find the maximum integral value of k for which the above quadratic equation has two distinct real roots.

 Jan 25, 2021
 #1
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kx^2  - 17x  + 2k   = 0

 

If this has  two real distinct roots, the discriminant must  be >   0

 

So

 

(-17)^2  - 4(k)(2k)  >  0

 

289  -  8k^2   >   0

 

289   >    8k^2

 

289/8  >   k^2          take the  positive root

 

sqrt (289/8)  >  k

 

≈ 6.01  >  k

 

So....the max integral value for k   =  6

 

 

cool cool cool

 Jan 25, 2021

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