Question

verify that 1/2, 1, -2 are the zeros of cubic polynomial 2x^3+x^2-5x+2 and verify the relationship between the zeros and coefficient​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer and Step-by-step explanation:

Putting x = 1/2 in eqn., we get,

$2(1/2)^3 + (1/2)^2 - 5(1/2) + 2$ = 2/8 + 1/4 -5/2 + 2

= 1/2 - 5/2 + 2 = -2 + 2 = 0

So, 1/2 is a root of the eqn. (verified)

Putting x = 1 in eqn., we get,

$2(1)^3 + (1)^2 - 5(1) + 2$ = 2 + 1 -5 + 2 = 5 - 5 = 0

So, 1 is a root of the eqn. (verified)

Putting x = -2 in eqn., we get,

$2(-2)^3 + (-2)^2 - 5(-2) + 2$ = -16 + 4 + 10 + 2 = 16 - 16 = 0

So, -2 is a root of the eqn. (verified)

Now, sum of roots  = 1/2 + 1 - 2 = -1/2

-b/a = -1/2

Hence, sum of roots = -b/a (verified)

sum of roots taken two at at time = 1/2*1 + 1*(-2) + (-2)*1/2 = 1/2-2-1 = -5/2

c/a = -5/2

Hence, sum of roots taken two at at time = c/a (verified)

product of roots  = 1/2 * 1 * (-2) = -1

-d/a = -2/2 = -1

Hence product of roots = -d/a (verified)