Which of the following is a polynomial with roots – - sqrt 5, sqrt 5 , and –3 ?

x3 – 2x2 – 3x + 6

x3 + 2x2 – 3x – 6

x3 – 3x2 – 5x + 15

x3 + 3x2 – 5x – 15

Question

Which of the following is a polynomial with roots – - sqrt 5, sqrt 5 , and –3 ?

x3 – 2x2 – 3x + 6

x3 + 2x2 – 3x – 6

x3 – 3x2 – 5x + 15

x3 + 3x2 – 5x – 15

anonymous · Answer

The roots +/- sqrt5 come from the difference of squares; the root of -3 comes from the binomial x+3, so we have$$\left( x^2-5 \right)(x+3)=x^3+3x^2-5x-15$$which is the last polynomial on the answer list.