is m the slope? what formula i may use to solve for this?

- July 30th 2012, 09:13 PMrcsfind the values of m so that the equation will have two equal roots.
is m the slope? what formula i may use to solve for this?

- July 30th 2012, 09:41 PMrichard1234Re: find the values of m so that the equation will have two equal roots.
Just because the textbook says does not mean you should automatically assume is the slope. Besides, what slopes are mentioned in this problem?

- July 30th 2012, 09:51 PMrcsRe: find the values of m so that the equation will have two equal roots.
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?

thanks - July 30th 2012, 09:56 PMrichard1234Re: find the values of m so that the equation will have two equal roots.
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. - July 30th 2012, 10:20 PMrcsRe: find the values of m so that the equation will have two equal roots.
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?

thanks - July 30th 2012, 10:37 PMrichard1234Re: find the values of m so that the equation will have two equal roots.
There should be a in there, i.e.

, this factors. If it didn't factor, how would you solve it then? - July 30th 2012, 10:52 PMrcsRe: find the values of m so that the equation will have two equal roots.
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? :) - July 30th 2012, 11:13 PMDevenoRe: find the values of m so that the equation will have two equal roots.
in that case, check your answer:

m = 4:

4(x^{2}+ 1) = 1 - (4√3)x

4x^{2}+ 4 = 1 - (4√3)x

4x^{2}+ (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(x^{2}+ 1) = 1 - (4√3)x

-3x^{2}- 3 = 1 - (4√3)x

3x^{2}+ (4√3)x + 4 = 0

again, this "ought" to factor as:

(√3x + 2)^{2}= 0. does it? - July 30th 2012, 11:23 PMrcsRe: find the values of m so that the equation will have two equal roots.
thanks Deveno