Use D'Alembert's Rational Roots Theorem. Any rational roots of the form of p/q (p and q assumed to be relatively prime) must be such that p divides the constant term (in this case 4) and q divides the coefficient of the largest power of x (in this case 1).
So, the candidate roots are ±1, ±2, and ±4. If you try these, you see that
x = -1 and x = 2 are roots. There are no other roots, but there must be three roots when we count by multiplicity. So, one of the two roots we found must have a multiplicity of 2.
It isn't difficult to see that this must be the root x = 2, because then you get the correct factorization:
Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with
Factor this polynomial: F(x)=x^3-x^2-4x+4 Try to find the rational roots. If p/q is a root (p and q having no factors in common), then p must divide 4 and q must divide 1 (the coefficient of x^3). The rational roots can thuis be
3x^4 + 5x^2 - 2 = 0 give imaginary and real roots rational roots theorem factors of (+-)p/q are possible rational zeros of function f where the coefficients of f are integers. how do you go about solving this?
List all possible rational zeros of... h(x)= 2x to the (4th power) - 5x (to the third power) + 3x (to the 2nd power) + 4x - 6 Use the Rational Roots Theorem. Any root of the form p/q with p and q relatively prime must be such that
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^3-2x^2+7x+6. 3)Find
I HAVE THESE ANSWERS FOR THE PROBLEMS. COULD YOU DOUBLE CHECK PLEASE, THIS IS A PRACTICE QUIZ WHICH ISN'T A GRADE IT JUST HELPS ME GET READY FOR THE TEST. 1) a 2) b 3) d 4) a 5) d 1. Solve x^3 + 6x^2 + 13x + 10 = 0. a) –2 + 2i,