Question

for a polynomial p(x)=2x^3+5x^2-9 find alpha+beta+ gamma, alpha×beta+beta× gamma +gamma×alpha, alpha×gamma×beta​

Answer 1

Step-by-step explanation:

Given :-

The Cubic Polynomial P(x) = 2x³+5x²-9

To find :-

Find the values of the following :

i) α+β+ γ

ii) α β + β γ + α γ

iii) α β γ

Solution :-

Given that

The Cubic Polynomial P(x) = 2x³+5x²-9

It can be written as

P(x) = 2x³+5x²+0x-9

On comparing this with the standard Cubic Polynomial ax³+bx²+cx+d then

a = 2

b = 5

c = 0

d = -9

If α, β, γ are the zeroes of the given Polynomial then

I) Sum of the Zeroes = -b/a

=> α+ β+ γ = -5/2

ii) Sum of the product of the two zeroes taken at a time = c/a

=> α β + β γ + α γ = 0/2 = 0

iii) Product of the zeroes = -d/a

=> α β γ = -(-9)/2

=> α β γ = 9/2

Answer :-

I) α+ β+ γ = -5/2

ii)α β + β γ + α γ = 0

iii)α β γ = 9/2

Used formulae:-

• The standard Cubic Polynomial is ax³+bx²+cx+d
• Sum of the Zeroes = -b/a
• Sum of the product of the two zeroes taken at a time = c/a
• Product of the zeroes = -d/a