Question

Sum and product of two zeroes of x4 – 4x3 – 8x2 + 36x – 9 are 0 and – 9respectively. Find the sum and product of its other two zeroes

Answer 1

Answer:

Sum of other two zeroes is 4 and product is 1

Step-by-step explanation:

Given that sum and product of two zeroes of $x^4 - 4x^3 - 8x^2 + 36x - 9$ are 0 and - 9 respectively.

we have to find the sum and product of its other two zeroes.

Let α, β, Ф, ω are the zeroes of given polynomial

Given α+β=0 and α.β=9

$x^4 - 4x^3 - 8x^2 + 36x - 9$

Now,

$\text{sum of zeroes=}\frac{-b}{a}=\frac{-(-4)}{1}=4$

$\text{Product of zeroes=}\frac{e}{a}=-9$

α + β + Ф + ω=4

⇒  Ф + ω=4

α. β.Ф.ω=-9

⇒ 9.Ф.ω=9 ⇒ Ф.ω=1

Sum of other two zeroes is 4 and product is 1