Question

If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the other two zeroes is

Answer 1

Answer:

If one of the zeroes of the cubic polynomial x3 + ax² + bx + c is -1, then the product of the other two zeroes is

Answer 2

Answer:

Product of the other two zeroes = -c

Step-by-step explanation:

Let the zeroes for a cubic polynomial ax³ + bx² + cx + d = 0 be α, β and γ

Now one zero is given as -1.

Let α = -1 .......  eqn 1

For our cubic polynomial x3 + ax² + bx + c, a=1, b=a, c=b and d=c

We know that Product of the zeroes αβγ for ax³ + bx² + cx + d = -d/a

Here, we will simply substitute the values

Product = -d/a = c/1 = c

∴ Product  = c ......  eqn 2

Now, Product  of the zeroes = αβγ = -βγ      ( ∵α = -1)

But Product  = c      (from eqn 2)

∴ -βγ = c

∴ Product of the other two zeroes = -c