Question

if α,β and gamma are the zeroes of the polynomial f(x)=ax³+bx²+cx+d, then 1/α+1/β+1/gamma=?
a)-b/a
b)c/d
c)-c/d
d)-c/a

Answer 1

Answer:

c)-c/d

Step-by-step explanation:

let alpha be x, beta be y and gamma be z

so 1/aplha + 1/beta + 1/gamma = 1/x + 1/y + 1/z

1x + 1/y + 1/z= yz+xz+xy/xyz

We know that

i)xy+yz+xz= c/a &

ii)xyz=-d/a

Substituting the values..we get

xy+xz+yz/xyz=c/a ÷-d/a

=c/a X -a/d

cancelling both a's we get c/-d..which is -c/d

Giving us the right answrr