Given that A

Question

Given that A < B, and x 4 + 3x 3 + 5x 2 + 5x + 2 = (x 2 + Ax + B)( x 2 + Bx + A), find A and B.

Quizplus · Accepted Answer

Expanding the right side of the equation, we get: $x^4 + (A+B)x^3 + (2AB + A + B)x^2 + (AB^2 + A^2B)x + A^2B^2$. Comparing coefficients with the left side, we have:1. $A + B = 3$2. $2AB + A + B = 5$3. $AB^2 + A^2B = 5$4. $A^2B^2 = 2$From 1, we can substitute $B = 3 - A$ into 2 to find $A$ and $B$. Doing so, we get $2A(3-A) + A + (3-A) = 5$, which simplifies to $6A - 2A^2 + 2 = 5$, and further to $2A^2 - 6A + 3 = 0$. Solving this quadratic equation for $A$, we find $A = 1$ and $B = 2$ by substituting back into $B = 3 - A$.

Given That a < B, and X4 + 3x3+ 5x2

Given That a < B, and X₄ + 3x₃+ 5x₂