Question

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

Answer 1

Step-by-step explanation:

Given : If x = -1/2 is a zero of the polynomial p (x) = 8x³ - ax² - x + 2.

To find : The value of a.

On putting x = - ½ in the given polynomial :

p (x) = 8x³ - ax² - x + 2

p(-½) = 8(-½)³ - a × (-½)² - (-½) + 2

p(-½) = 8(-⅛) - a × (¼) + ½ + 2

p(-½) = - 1 - a/4 + ½ + 2

p(-½) = - 1 + ½ + 2 - a/4

p(-½) = 1 + ½ - a/4

p(-½) = 3/2 - a/4

Given that x = - ½ is a root of p(x). :

p(-½) = 0

Therefore,

3/2 - a/4 = 0  

a/4 = 3/2

2a = 3 × 4

a = (3 × 4)/2

a = 3 × 2

a = 6  

Hence, the value of a is 6.

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