Which of the following is a polynomial with roots – square root of 3, square root of 3, and 2?
Which of the following expressions represents a polynomial with roots at -√3, √3, and 2?
- (x^3 + 3x^2 - 5x - 15)
- (x^3 + 2x^2 - 3x - 6)
- (x^3 - 3x^2 - 5x + 15)
- (x^3 - 2x^2 - 3x + 6)
3 Answers
1) x^3+3x^2-5x-15=0 has 3 distinct real roots:
x=-3, x=+/- 2.236068=+/-sqrt(5)
2) x^3+2x^2-3x-6=0 has 3 distinct real roots:
x=-2, x=+/- 1.732051=+/- sqrt(3)
3) x^3-3x^2-5x+15=0 has 3 distinct real roots:
x=3, x=+/-2.236068=+/-sqrt(5)
4) x^3-2x^2-3x+6=0 has 3 distinct real roots:
x=2, x=+/- 1.732051=+/-sqrt(3). Answer.
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