Question

if alfa,betaand gamma are zeros at p(x) =1/2xcube -5xsq-11x-3,then alfa+beta+gamma =....?​

Answer 1

Answer:

See the explanation,

Step-by-step explanation:

p(x) = (1x³/2) - 5x² - 11x - 3

We know the general form of a cubic polynomial is ax³+bx²+cx+d=0

So in the given polynomial,

a=1/2

b= -5

c= -11

d= -3

Multiplying the polynomial with 2 can make the equation easy to solve. So after multiplying with 2 , we will get:-

2x³-10x²-22x-6

Now,

a = 2

b = -10

c = -22

d = -6

Now there are certain relationships between zeroes and coefficients of a cubic polynomial,

Which are as follows:-

(sum of roots ) = -b/a

(sum of product of roots) = c/a

(product of roots) = -d/a

By using the first relationship,

We have,

Alfa + Beta + Gamma = -b/a

→ -(-10)/2

→10/2

→5

So, alfa+beta+gamma=5