Question

If aby are the zeros of the polynomial f(x)=ax^3 +bx^2 + cx +d then 1/a + 1/b + 1/y=?​

Answer 1

I have gave you a correct answer so please mark me as brainlist

Answer 2

Answer:

Qᴜᴇsᴛɪᴏɴ :-

if a,b and y are the zeros of the polynomial f(x)=ax^3 +bx^2 + cx +d then 1/a + 1/b + 1/y = ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

For a cubic equation ax³+ bx² +cx+ d = 0 let p,q and r be its roots, then the following holds :-

p + q + r = (-b/a)

pq + qr + pr = c/a

p * q * r = (-d/a) .

Sᴏʟᴜᴛɪᴏɴ :-

from above told formula , when roots are a, b & y, we get :-

→ (ab + by + ay) = c/a -------- Equation (1)

→ a * b * y = (-d/a) ------------ Equation (2)

Now,

→ 1/a + 1/b + 1/y

Taking LCM ,

→ (by + ay + ab) / (aby)

Or,

→ (ab + by + ay) / aby

Putting values of Equation (1) & (2) Now, we get,

→ (c/a) / (-d/a)

→ (c/a) * (-a/d)

→ (-c/d) (Ans.)

hope it helps u buddy ...

pls mark me as brainliest