Question

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

Answer 1

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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Answer 2

$\huge \fcolorbox{red}{pink}{Solution :)}$

Given ,

The polynomial is P(x) = 8x³ - ax² - x + 2 and its root is x = -1/2

i.e P(-1/2) = 0

Therefore ,

$\sf \hookrightarrow 8 {( - \frac{1}{2}) }^{3} - a {( - \frac{1}{2}) }^{2} - ( - \frac{1}{2} ) + 2 = 0 \\ \\\sf \hookrightarrow - 1 - \frac{a}{4} + \frac{1}{2} + 2 = 0 \\ \\ \sf \hookrightarrow \frac{ - 4 - a + 2 + 8}{4} = 0 \\ \\\sf \hookrightarrow 6 - a = 0 \\ \\ \sf \hookrightarrow a = 6$

Hence , the value of a is 6

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