​If 2 is a zero of the polynomial p(x) = x³+ 3x²- 6x - a, then what is the sum of the squares of the other zeros of the polynomial?​

Correct option is B

Given:

Polynomial: p(x) = x³+ 3x²- 6x - a

One zero of the polynomial: x = 2

Concept Used:

If x = 2 is a zero of the polynomial, then p(2) = 0.

Solution:

Since x = 2 is a zero,

p(2) = 0:

=> 2³+ 3(2)²- 6(2) - a = 0

=> 8 + 12 - 12 - a = 0

=> 8 - a = 0

=> a = 8

Now, P(x) =  x3 + 3x2 - 6x - 8

Since 2 is the zero of the polynomial, so P(x) can be factorized as

P(x) =  x3 + 3x2 - 6x - 8 = (x -2)( x² + 5x + 4)

Now, 

( x2 + 5x + 4)

=> (x2 + 4x + x + 4)

=>  x(x + 4) + 1(x + 4)

=> (x + 4)(x +1)

So, other zeroes are -4 and -1

Thus, 

Sum of the squares of the other zeros of the polynomial

=> (-4)² + (-1)²

=> 16 + 1 = 17 

∴ The correct answer is 17.