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

- Jul 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?

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

- Jul 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 - Jul 30th 2012, 09:56 PMrichard1234Re: find the values of m so that the equation will have two equal roots.
Okay, so $\displaystyle m = \frac{1 - 4 \sqrt{3}x}{x^2 + 1}$. But does get you any closer to a solution?

I would start with the original equation and expand the LHS, yielding

$\displaystyle mx^2 + m = 1 - 4 \sqrt{3} x$

$\displaystyle mx^2 + 4 \sqrt{3} x + (m-1) = 0$

This has two equal roots if and only if the discriminant is zero. - Jul 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 - Jul 30th 2012, 10:37 PMrichard1234Re: find the values of m so that the equation will have two equal roots.
There should be a $\displaystyle 4 \sqrt{3}$ in there, i.e.

$\displaystyle D = (4 \sqrt{3})^2 - 4m(m-1) = 0$

$\displaystyle 48 - 4m^2 + 4m = 0$

$\displaystyle m^2 - m - 12 = 0$, this factors. If it didn't factor, how would you solve it then? - Jul 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? :) - Jul 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? - Jul 30th 2012, 11:23 PMrcsRe: find the values of m so that the equation will have two equal roots.
thanks Deveno