Question

if x=-1/2 is root of a polynomial g(x)=8x³-ax²-x+2. find the value of A​

Answer 1

Answer:

Given- 1/2 is root of polynomial

- g(x) 8x^3-ax^2-x+2

To find - Value of A

note- as we now a root of a polynomial is a no. from which the whole polynomial become zero

Solution- g(-1/2)= 8x^3-ax^2-x+2

8(-1/2)^3-a(-1/2)^2-x+2= 0

8(-1/8)-a(1/4)-(-1/2)+2=0

-1-a/4+1/2+2=0

-a/4= 1-2-1/2

-a/4= (-1)-1/2 (LCM of 2 & 1 is 2)

-a/4= -2-1/2

-a/4= (-3/2)

-a= (-3/2)×4

a= 3/8

Answer 2

g(x) = 8x^3 - ax^2-x+2

= 8× (-1/2)^3 - a× (-1/2)^2-(-1/2)+2

= 8 × -1/8 - a× -1/4 + 5/2

= -1 + a/4 +5/2

-a/4 = -1 +5/2

-a/4 = 3/2

By cross multiplication method

-2a = 12

a = 12/-2

a= -6