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Mathematics Question on Integrals of Some Particular Functions

The number of integral values of m for which the equation (1+m2)x2−2(1+3m)x+(1+8m)=0(1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0 has no real root is :

A

infinitely many

B

2

C

3

D

1

Answer

infinitely many

Explanation

Solution

D<0  4(1+3m)2−4(1+m2)(1+8m)<0D < 0 \; 4(1 + 3m)^2 - 4(1 + m^2)(1 + 8m) < 0 ⇒  m(2m−1)2>0  ⇒  m>0\Rightarrow \; m(2m - 1)^2 > 0 \; \Rightarrow \; m > 0