Find a polynomial of degree 3 whose zeros are -3, 3/2 and 2
a.2x^3-15x-18
b.2x^2+3x-9
c.2x^2-7x+6
d.2x^3-x^2-15x+18
e.2x^3-7x^2-15x+18
I know C and B are not options because the degree is not three, but how do I figure out the rest?
Find a polynomial of degree 3 whose zeros are -3, 3/2 and 2
a.2x^3-15x-18
b.2x^2+3x-9
c.2x^2-7x+6
d.2x^3-x^2-15x+18
e.2x^3-7x^2-15x+18
I know C and B are not options because the degree is not three, but how do I figure out the rest?
Do you know about the factorial decomposition of polynomials?
If a polynomial of degree 3 has 3 real roots, letīs say then you can write it down as where is the leading coefficient of your polynomial.
Obviously, this fact gets generalised for any polynomial of degree n with m roots, .
That means that you can write your polynomial as since they didnīt tell you explicitly nothing about the leading coefficient of the polynomial, might be any real number different of zero. So set since all your options have L.C.=2.
Apply distributive law (if you have trouble with that tell me and Iīll write it down) and you get option d.