Solve for roots using theory of equations-
x^4 - 16x^3 + 86x^2 - 176x + 105 = 0 , where two roots are 1 and 7.Find the others.

Question

Solve for roots using theory of equations-
x^4 - 16x^3 + 86x^2 - 176x + 105 = 0 , where two roots are 1 and 7.Find the others.

anonymous · Answer

@dpaInc

anonymous · Answer

since you already know two roots, you can reduce that to a quadratic, correct?

anonymous · Answer

but i want by the method of sum of roots and product of roots.

anonymous · Answer

the product of the roots is 105...
but i'm not familiar with the "sum of roots" for a fourth degree polynomial... sorry..

anonymous · Answer

i think u can divide the 4th degree polynomial by (x-1)(x-7) and it reduce to a 2nd degree polynomial .

anonymous · Answer

ok... i googled it....

7 * 1 * r1 * r2 = 105
7 + 1 + r1 + r2 = 16 <--- b/a

two equations, two unknowns... solve the system for r1 and r2....

anonymous · Answer

so 
r1 * r2 = 15
r1 + r2 = 8
can you take it from here?

anonymous · Answer

ok