If 3x2+2αxy+2y2+2ax-4y+1 can be resolved into two linear factors, prove that α is the root of the equation x2+ 4ax+2a2+6=0.

please don't solve the problem

just hint is expected.

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- Aug 16th 2011, 07:13 PMsumedhproblem of quadratic equation with two variables
If 3x2+2αxy+2y2+2ax-4y+1 can be resolved into two linear factors, prove that α is the root of the equation x2+ 4ax+2a2+6=0.

please don't solve the problem

just hint is expected. - Aug 16th 2011, 11:34 PMFernandoRevillaRe: problem of quadratic equation with two variables
- Aug 17th 2011, 03:26 AMHallsofIvyRe: problem of quadratic equation with two variables
That is, if you meant "can be resolved into two linear factors"

**with rational coefficients**. - Aug 17th 2011, 04:28 AMFernandoRevillaRe: problem of quadratic equation with two variables
- Aug 17th 2011, 08:37 AMsumedhRe: problem of quadratic equation with two variables
on solving i got

α^2 y^2+a^2+2aαy =-6y^2-3+12y [α means alpha]

α^2 y^2+a^2+2aαy -9 (y-3)^2

after equating what should i do???

could you please tell me the concept for solving this???? - Aug 17th 2011, 09:29 AMFernandoRevillaRe: problem of quadratic equation with two variables
The discriminant of the equation is then,

is a perfect square iff the discriminant of is . Now, verify . Equivalently, is a root of . - Aug 19th 2011, 11:49 PMsumedhRe: problem of quadratic equation with two variables
thank you very much i got it