Question

Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial

p(x) = 2x3
- 3x2
- 3x + 2 and then verify the relationship between the

zeroes and the coefficients.

Answer 1

The answer is "2, and 1/2 is not a part of polynomial".

Explanation:

Given equation:

`P(x) = 2x^3-3x^2-3x+2\\`

put the value 2, -1, and 1/2 in above equation we get:

p(2) = 0

p (-1)= 0

p (1/2) = 0

compare the above equation with:
`ax^3+bx^2+cx+d= 0`

a= 2

b= -3

c=-3

d= 2

`i) \ \alpha \beta+ \beta\gamma+\gamma \alpha= (c)/(a)\\\\ ii) \ \alpha +\beta +\gamma= (-b)/(a)\\\\ iii) \ \alpha \beta \gamma= (-d)/(a)\\\\`

`i) 2 * -1 + -1 * (1)/(2) + (1)/(2) * 2 = (-(3))/(2)\\\\-2- (1)/(2)+1= (-3)/(2)\\\\(-4-1+2)/(2) = (-3)/(2) \\\\(-3)/(2) =(-3)/(2)\\`

`ii) \ 2 + (-1) + (1)/(2) = (-(-3))/(2)\\\\2-1+(1)/(2) = (3)/(2)\\\\(4-2+1)/(2)= (3)/(2)\\\\(3)/(2)=(3)/(2)\\\\`

`iii) 2 * -1 * (1)/(2) = (-2)/(2)\\\\ -1 =-1`