Question

If (−2) is a zero of the polynomial P(x)=x^3+ax^2-4x-12 , then find the value of a.

Answer 1

Answer:

a = 3

Step-by-step explanation:

It is given that -2 is the zero of x³ + ax² - 4x - 12.

So when x is substituted as -2, the value of the expression would be equal to 0. This is known as 'Factor Theorem'

Applying this theorem,

p(x) = x³ + ax² - 4x - 12

When x = -2

p(-2) = (-2)³ + a(-2)² - 4(-2) - 12 = 0

⇒ -8 + 4a + 8 - 12 = 0

⇒ 4a - 12 = 0

⇒ 4a = 12

⇒ a = 12 ÷ 4

⇒ a = 3

∴ The value of a = 3

Answer 2

Answer:

$\huge \green{ \boxed{ \sf \: a = 3}}$

Explanation :

Given,

$\sf \: p(x) = {x}^{3} + a {x}^{2} - 4x - 12$

and

- 2 is a zero of the polynomial.

So, (x+2) is a factor of the polynomial.

Now, if we assumed that, x = -2 and put this in the polynomial, then P(x) = 0 or P(-2) = 0

$\sf \: p( - 2) = {( - 2)}^{3} + a {( - 2)}^{2} - 4( - 2) - 12 = 0 \\ \sf \implies \: - 8 + 4a + 8 - 12 = 0 \\ \sf \implies \:4x = 12 \\ \sf \implies \:a = \frac{12}{4} \\ \therefore \: \sf a = 3$