Answer: Yes!
Explanation:
Answer: Yes, the other roots of the equations ax2+a2x+1=0 and bx2+b2x+1=0 will satisfy the equation abx2+x+a2b2=0.
To show this, let us assume that x1 and x2 are the other two roots of the equations ax2+a2x+1=0 and bx2+b2x+1=0 respectively. Then, substituting x1 and x2 in the equation abx2+x+a2b2=0, we get:
abx12 + x1 + a2b2 = abx22 + x2 + a2b2
Rearranging the terms, we get:
(abx12 - abx22) + (x1 - x2) = 0
Now, since x1 and x2 are the roots of the two equations, we can write:
a(x1 - x2) (bx1 - bx2) = 0
Therefore,
abx12 - abx22 + x1 - x2 = 0
Hence, we can conclude that the other roots of the equations ax2+a2x+1=0 and bx2+b2x+1=0 will satisfy the equation abx2+x+a2b2=0.