Question

(04.05 LC)

Which of the following is a polynomial with roots: −square root of 3 , square root of 3, and 2? (6 points)

Select one:
a. x3 + 3x2 − 5x − 15
b. x3 + 2x2 − 3x − 6
c. x3 − 3x2 − 5x + 15
d. x3 − 2x2 − 3x + 6

Answer 1

correct answer is option d.

Explanation:

Here, we have The following expression to check Which of the following is a polynomial with roots: −square root of 3 , square root of 3, and 2 :

a. x3 + 3x2 − 5x − 15

For
`-√(3)` ,
`x^(3) + 3x^(2) -5x -15` ⇒
`(-√(3)) ^(3) + 3(-√(3) )^(2) -5(-√(3) ) -15`
`\\eq 0` . So, this isn't the one. We move on further!

b. x3 + 2x2 − 3x − 6

For
`-√(3)` ,
`x^(3) + 2x^(2) -3x -6` ⇒
`(-√(3)) ^(3) + 2(-√(3) )^(2) -3(-√(3) ) -6` = 0 .

For
`√(3)` ,
`x^(3) + 2x^(2) -3x -6` ⇒
`(√(3)) ^(3) + 2(√(3) )^(2) -3(√(3) ) -6` = 0.

For 2 ,
`x^(3) + 2x^(2) -3x -6` ⇒
`(2) ^(3) + 2(2)^(2) -3(2 ) -6`
`\\eq 0` . So, this isn't the one. We move on further!

c. x3 − 3x2 − 5x + 15

For
`-√(3)` ,
`x^(3)- 3x^(2) -5x -15` ⇒
`(-√(3)) ^(3)- 3(-√(3) )^(2) -5(-√(3) ) -15`
`\\eq 0` . So, this isn't the one. We move on further!

d. x3 − 2x2 − 3x + 6

For
`-√(3)` ,
`x^(3) - 2x^(2) -3x +6` ⇒
`(-√(3)) ^(3) - 2(-√(3) )^(2) -3(-√(3) ) +6` = 0 .

For
`√(3)` ,
`x^(3) - 2x^(2) -3x +6` ⇒
`(√(3)) ^(3) -2(√(3) )^(2) -3(√(3) ) +6` = 0.

For 2 ,
`x^(3) - 2x^(2) -3x +6` ⇒
`(2) ^(3) - 2(2)^(2) -3(2 ) +6` = 0.

Therefore, correct answer is option d.