Just because the textbook says does not mean you should automatically assume is the slope. Besides, what slopes are mentioned in this problem?
no, im solving it this way that i have to divide both sides of the equation by x^2+ 1 then m = 1 - 4 sq. root of 3 x underneath x^2+1 sir may i know the next move for the value of m?
Okay, so . But does get you any closer to a solution?
I would start with the original equation and expand the LHS, yielding
This has two equal roots if and only if the discriminant is zero.
sir im solving for the discriminant.... that a = m, b = 4, and c = (m-1) is this correct? the equate to zero.
D = 4^2 - 4(m)(m-1)
D = 16 - 4m^2 + 4m
0 = 16 - 4m^2 + 4m
0 = -4(m^2-m-4)
0 = m^2-m-4 sir this not a factorable expression... what is the next sir?
if i were to solve it sir , i will use quadratic formula. is it ok?
factor like ( m - 4) (m + 3) = 0
then m = 4 or m = - 3
is that right sir?
in that case, check your answer:
m = 4:
4(x2 + 1) = 1 - (4√3)x
4x2 + 4 = 1 - (4√3)x
4x2 + (4√3)x + 3 = 0
since we are supposed to have 2 equal roots, this should factor as:
(2x + √3)2 = 0. does it?
m = -3:
-3(x2 + 1) = 1 - (4√3)x
-3x2 - 3 = 1 - (4√3)x
3x2 + (4√3)x + 4 = 0
again, this "ought" to factor as:
(√3x + 2)2 = 0. does it?