Question

What polynomial has roots of -1, -2, and 3 ? Will fan and give medal.

Answer 1

A. x3 + 6x2 + 11x + 6
B. x3 - x2 - 5x + 2
C. x3 + 2x2 - 7x + 2
D. x3 - 7x - 6

Answer 2

\[\alpha \beta \gamma=-\frac{D}{A}\]
where \[\alpha, \beta, \gamma\] are your roots and \[A\] is the coefficient of the cubic term, \[D\] is the constant term.
Multiply the roots simply and verify which polynomial is satisfying it

Answer 3

That doesn't make sense to me.

Answer 4

or you could just substitute in the values given, x=-1, x=-2, x=3

see which equation becomes zero when you substitute those values in

Answer 5

That is a formula which relates roots and coefficients of a polynomial.
For a quadratic polynomial you may have learned these formulae:
\[\alpha \beta=\frac{C}{A}\]\[\alpha+\beta=-\frac{B}{A}\]
For cubic you have
\[\alpha \beta \gamma=-\frac{D}{A}\]\[\alpha+\beta+\gamma=-\frac{B}{A}\]\[\alpha \beta+\beta \gamma+\alpha \gamma=\frac{C}{A}\]

Answer 6

You can also put the value of x, true but then you'd have to check all 3 roots

Answer 7

I'm on a timed test, I'm just gonna guess.