Algebra
posted by Marissa .
Can someone please explain how to do these problems.
1)write a polynomial function of least degree with intregal coefficients whose zeros include 4 and 2i.
2)list all of the possible rational zeros of f(x)= 3x^32x^2+7x+6.
3)Find all of the rational zeros of f(x)= 4x^33x^222x15.
Because all the coefficients of the polynomial are real, if 2i is a zero, then the complex conjugate 2i must also be a zero. This means that the least order polynomial is proportional to:
(x4)(x4i)(x+4i)= (x4)(x^2 + 16)=
x^3  4x^2 + 16 x  64
To find the rational roots, use the Rational Roots Theorem: if x = p/q is a rational root (and p and q don't have any divisors in common), then p must divide the constant term and q the coefficient of the highest power of x.
In case of the polynomial
3x^32x^2+7x+6.
Ths means that p is a divisor of 6 and q a divisor of 3.
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