Engineering
Mathematics
Quadratic Equation and Nature of Roots
Question
The number of integral values of m for which the equation (1 + m2) x2 – 2(1 + 3m) x + (1 + 8m) = 0 has no real root is
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Solution
D = 4 (1 + 3m)2 –4(1 + m2) (1 + 8m)
= 4(1 + 9m2 + 6m – 1 – 8m – m2 – 8m3)
= –8m (4m2 – 4m + 1)
=–8m(2m –1)2 < 0
Infinitely many values of m.