Explanation:

Correct 2: 17

To find the sum of the squares of the other zeros of the polynomial p(x)=x³+3x²−6x−a, we first need to determine the value of a using the fact that 2 is a zero of the polynomial. We substitute x=2 into the polynomial and set it equal to zero to find a. Then we can use Vieta's formulas to find the sum of the squares of the other zeros.

Step by Step Solution:

Step 1

Substitute x=2 into the polynomial: p(2)=2³+3(2²)−6(2)−a=0.

Step 2

Calculate p(2): p(2)=8+12−12−a = 8−a.

Step 3

Set the equation to zero: 8−a =0 which gives a = 8.

Step 4

Now the polynomial is p(x)=x³+3x²−6x−8. Using Vieta's formulas, if r1?=2 is one zero, then the sum of the other zeros r2?+r3?=−3 and the product r2?r3?=−8/2=−4.

Step 5

The sum of the squares of the other zeros is r₂²?+r₃²?=(r2?+r3?)²−2r2?r3?=(−3)²−2(−4)=9+8=17.

Final Answer: 17