SOLUTION: Find the value of k if (x^3-x^2-5x-2)(x^4+x^3+kx^2-5x+2)=x^7-4x^5-14x^4-5x^3+19x^2-4.
Algebra.Com
Question 1177973: Find the value of k if (x^3-x^2-5x-2)(x^4+x^3+kx^2-5x+2)=x^7-4x^5-14x^4-5x^3+19x^2-4.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
Find the value of if
....multiply left side
...............simplify
that will be true if
check:
which is true
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The answer can be obtained with FAR less work than shown by the other tutor....
In the equation, k is the coefficient of the x^2 term. So look at ANY one coefficient in the product of a term which is x^2 or a higher power of x.
Example: The coefficient of the x^2 term in the product is 19. That coefficient comes from (1) the constant term in the first expression times the x^2 term in the second, (2) the product of the linear terms in the two expressions, and (3) the x^2 term in the first expression and the constant term in the second:
ANSWER: k=2
I could have used any other coefficient of the product of a term with degree 2 or higher.
Second example, using the coefficient of the x^4 term in the product:
RELATED QUESTIONS
Find the value of k if (x^3-x^2-5x-2)(x^4+x^3+kx^2-5x+2)=x^7-4x^5-14x^4-5x^3+19x^2-4.... (answered by Fombitz)
x^4-5x^3-14x^2 (answered by Alan3354)
Determine the value of k in f(x) = 5x^3+kx^2-4x+4 so that x+2 is a factor (answered by MathLover1)
if x^6+kx^5+x^4+kx^3+3x^2-k+2 is a multiple of (x-k) find the value of... (answered by jsmallt9)
1. Find k so that x+5 is a factor of x^3+5x^2-kx-20.
2. Find k so that x-7 is a factor... (answered by Edwin McCravy)
3/2 (5x+7)-4=2/5... (answered by Boreal)
(x^3-5x^2+4x-7)divided... (answered by rfer)
(7/x^2-5x)+(3/5-x)=(4/x) (answered by RAY100)
4x^4-19x^3-5x^2 (answered by stanbon)