Question

Find the sum, Product
and sum of the
Product
the two zeroes of
x^3+ 4x²-5x-2​

Answer 1

Step-by-step explanation:

sum of zeroes is -b/a it is 4. a is1 b is 4 c is -5 and dis -2

sum of the products is c/a it is -5

products is -d/a it is 2

if it is helpfull plz make me as brainliest

Answer 2

Answer:

(ii) Given : g(x) = x³ - 4x² + 5x - 2; 2,1,1

On comparing with ax³ + bx² + cx + d ,

a = 1 , b= -4 ,c = 5 , d =- 2

(a) On putting x = 2 in the given polynomial,

g(2) = (2)³ - 4(2)² + 5(2) - 2

= 8 – 16 + 10 – 2  

= - 8 + 8

= 0

(b) On putting x = 1 in the given polynomial,

g(1) = (1)³ - 4(1)² + 5(1) –2

= 1 – 4 + 5 – 2

= -3 +3  

= 0

Hence, 2,1,1 are the Zeroes of the polynomial x³ - 4x² + 5x - 2.

Let α,β,γ are the three Zeroes of the  polynomial.

α = 2, β = 1, γ =1

Sum of zeroes = −coefficient of x² / coefficient of x³

α + β + γ = −b/a

2+1+1=−(−4)/1

4 = 4

Product of the zeroes = - constant term / coefficient of x²

α β γ = - d/a

αβγ = –(−2)

2×1×1 = 2

2 = 2

sum of the product  of its zeroes taken two at a time = coefficient of x / coefficient of x³

αβ+βγ+αγ = ca

2×1+ 1×1 + 1×2 = 5/1

2 + 1 + 2 = 5

5 = 5

Hence, relationship between the Zeroes and the coefficients is verified.

HOPE THIS ANSWER WILL HELP YOU....

ℏ✺℘ḙ ʏ✺ṳ ❡ḙт ʏ✺ṳԻ ᾰℵṧωḙԻṧ

℘ℓℨ ՊᾰԻк ᾰṧ ♭Իᾰ!ℵℓ!ṧт