Question

Find Sum and Product of Roots for

X^4 -6x^3+12×^2-12x+4 = 0



Hint :
If u, v, w, and z representthe roots of the Quartic polynomial ax4 + bx3 + cx2 + dx +e = 0,

then the following relationships are true:

(a) u + v + w + z = −b/a,
(b) u(v + z) + v(w + z) + w(u + z) = c/a (c) u(vw + wz) + v(uz + wz) = −d/a
and
(d) u · v · w · z = e/a

Can we Use above to actually solve for Root?​

Answer 1

Step-by-step explanation:

Given bi quadratic equation is

X^4 -6x^3+12×^2-12x+4 = 0

On comparing with ax4 + bx3 + cx2 + dx +e = 0,

we have , a =1;b=-6;c=12;d=-12;e=4

If u, v, w, and z representthe roots of the Quartic polynomial ax4 + bx3 + cx2 + dx +e = 0,

then

Sum of the roots

=u+v+w+z=-b/a

=-(-6)/1

=6

Sum of the roots=6

Product of the roots

=uvwz

=e/a

=4/1

=4

Product of the roots =4

Answer 2

hope it helps............