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Question

If the roots of the equation (m2)x2(82m)x(83m)=0 are real and opposite in sign, then the number of integral value(s) of m is

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Solution

(m2)x2(82m)x(83m)=0
m20 as the equation has two roots.
x2(82mm2)x(83mm2)=0
Let f(x)=x2(82mm2)x(83mm2)
Since, roots are opposite in sign, hence 0 lies between the roots.
f(0)<0
(83mm2)<0
(m2)(3m8)<0
m(2,83)
Hence, no integral value of m in this interval.

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