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The number of integral values of m for w...

The number of integral values of m for which the equation `(1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0,` has no real roots is

A

3

B

infinitely many

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Key idea
(i) First convert the given equation is quadratic equation.
(ii) Use, Discriminant, `D=b^(2)-4ac lt0`
Given quadratic equation is
`(1+m^(2))x^(2)-2(1+3m)x+(1+8m)=0" "...(i)` Now, discriminant
`D=[-1(1+3m)]^(2)-4(1+m^(2))(1+8m)`
`=4[(1+3m)^(2)-(1+m^(2))(1+8m)]`
`=4[1+9m^(2)+6m-(1+8m+m^(2)+8m^(3))]`
`=4[-8m^(3)+8m^(2)-2m]`
`=-8m(4m^(2)-4m+1)=-8m(2m-1)^(2)`
According to the question there is no solution of the quadratic Eq. (1,) then,
`D lt0`
`therefore-8m(2m-1)^(2)lt0impliesmgt0`
So, there are infinitely many values of 'm' for which, there is no solution of the given quadratic equation.
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