Perfect squares Polynomials

Algebra Level 4

$lx^2+mx+n \\ mx^2+nx+l \\ nx^2+lx+m$

For distinct non-zero values of $l,m$ and $n$ . It is given that all of the algebraic expressios above are perfect square polynomials, find the value of $\dfrac{l +m}n$ .

4 1 6 -6 None of these choices -4 8

1 solution

Harish Yadav
Jan 30, 2015

First using discriminant formula we get
0 = m^2-4nl i
0 = n^2-4ml ii
0 = l^2-4mn iii
From i & iii we get
m^2 -4nl=l^2-4mn
m^2-l^2=4nl-4mn
(m+l)(m-l)=-4n(m-l)
(m+l)=-4n
therefore, (m+l)/n =-4

Can you add more details? How does the discriminant help?

Calvin Lin Staff - 6 years, 4 months ago

thanks sir

Harish Yadav - 6 years, 4 months ago

Thanks! I moved your comment into the solution. You can edit your solution by selecting "edit" at the bottom.

FYI To start a new line, add 3 empty spaces to the end of your line.
I edited your text, so you can refer to it (just click on edit to see!)

Calvin Lin Staff - 6 years, 4 months ago

@Calvin Lin – sir can you post the solution of my problem powers and powers everywhere

Harish Yadav - 6 years, 4 months ago

There are actually no solutions to this system, hence the answer is "none of these". See the report forum.

I have updated the answer to "none of these".

Calvin Lin Staff - 6 years, 4 months ago

sir can you please tell me the reason why answer is none of these

Harish Yadav - 6 years, 4 months ago

See Jon Haussmann's report in the report forum. Click on the "dot dot dot" menu, and select "view disputes".

Please ensure that you are receiving email from us, so that you are aware when people report your problem.

Calvin Lin Staff - 6 years, 4 months ago

Perfect squares Polynomials

1 solution

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