The title means that the roots of p(q(x))=0 are -23, -2 1,-17,-15, and the roots of q(p(x))=0 are -59, -57,-5/kloc. Is that what you mean?

Let p(x)=x? +ax+b，q(x)=x？ +cx+d

Then q (x1)+q (x2) =-a/2inp (q (x)) = 0inq (x1)+q (x2) =-c/2.

The root of p(q(x))=0 is actually

x？ +cx+d=q(x 1) and x? +CX+d = the root of q (x2)

There are q (x11)+q (x12) = q (x 21)+q (x22) =-c/2, so)-c/2 =-23-/kloc-.

c=76

Similarly, a=2 16 can be obtained.

According to the product of the roots of quadratic equation, there are 21*17 = d-q (x1) and 23 * 15 = D-Q (x2) (the two values are interchangeable).

The addition of the two formulas gives 21*17+23 *15 = 2d-q (x1)+q (x2) = 2d+a/2, and d=8 10.

B=5836 can be obtained in the same way.

So p(x)+q(x)=2x? +292x+6646=2(x+73)？ -2006 & gt=-40 12