Question

If x = 1/2 is a zero of the polynomial f(x) =8x³ +ax²-4x+2, find the value of a.

Answer 1

Given : If x = 1/2 is a zero of the polynomial p (x) = 8x³ + ax² - 4x + 2 .

To find: The value of a.

On putting x =  ½ in the given polynomial :

p (x) = 8x³ + ax² - 4x + 2

p(½) = 8(½)³ + a × (½)² -4 (½) + 2

p(½) = 8(⅛) + a × (¼) - 4/2 + 2

p(½) = 1 +  a/4 - 2 + 2

p(½) = 1 + a/4

Given that x =  ½ is a root of p(x) :

p(½) = 0

Therefore,

1 + a/4 = 0  

a/4 = - 1

a = - 1 × 4

a = - 4

Hence, the value of a is - 4.

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Answer 2

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putting the value of x =  ½

p (x) = 8x³ + ax² - 4x + 2

p(½) = 8(½)³ + a × (½)² -4 (½) + 2

p(½) = 8(⅛) + a × (¼) - 4/2 + 2

p(½) = 1 +  a/4 - 2 + 2

p(½) = 1 + a/4

Now,

1 + a/4 = 0  

a/4 = - 1

a = - 1 × 4

a = - 4

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

https://brainly.in/question/15903502