You are here:

Algebra/square root


If x^4 + lx^3+ mx^2+12x+9 is a perfect square
then find value of l and m? Here ^ denotes exponent.?
In exercise we have to find square root by division
or factorization method

Yes, the ^ symbol denotes an exponent.
To be a perfect square, we need (ax^2 + bx + c)^2 to be what's given.
Squaring this gives [1] ax^4 + 2abx^3 + (2ac+b)x^2 + 2bcx + c^2.

This says that since we have x^4, the value of a is 1.
This says that since we have a constant 9, and c^2 = 9, so c = 3 (or -3).

Putting in a=1 and c=3 into the [1] gives x^4 + 2bx^3 + (2+b)x^2 + 6bx + 9.
Since the value of the x term is 12x and it is also 2bx, this says 2b = 12, so b is 6.

Putting this in gives x^4 + 12x^3 + 8x^2 + 36x + 9.
This gives the value 12 to l and the value 8 to m.  


All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.


I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

Documents at Boeing in assistance on the manufacturiing floor.

MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

Awards and Honors
Both my BS and MS degrees were given with honors.

Past/Present Clients
Students in a wide variety of areas since the 80's; over 1,000 of them have been in algebra.

©2016 All rights reserved.