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Question

If the quadratic equation x2+[a25a+b+4]x+b=0 has roots 5 and 1, then maximum value of [a] (where [a] denote the greatet integer function) is

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Solution

​​​​​​Since, 5 and 1 are the roots of the equation.
x2+[a25a+b+4]x+b=0
5+1=[a25a+b+4] and 5×1=b
[a25a+b+4]=4 and b = -5
[a25a5+4]=4
[a25a1]=44a25a1<5
a25a14 and a25a1<5
a25a50 and a25a6<0
a5352 or a5+352 and 1<a<6
a(1,5352][5+352,6)
[a]max=5

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