SOLUTION: sove each equation. state the number and type of roots. 3x + 8 = 0 Write a polynomial function of least degree with integral coefficients that has the given zeros -4, 1, 5

Question 278564: sove each equation. state the number and type of roots.
3x + 8 = 0
Write a polynomial function of least degree with integral coefficients that has the given zeros
-4, 1, 5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
3x + 8 = 0
A first degree polynomial. With rational coefficients like this, these always have 1 rational root.

If "r" is a zero of a polynomial, then (x-r) is a factor of the polynomial. So if -4, 1 and 5 are to be roots, then (x-(-4)), (x-1) and (x-5) must be factors of the polynomial. And if we want a function "of least degree", then we do not want any more factors than these three. So this makes the function:
f(x) = (x+4)(x-1)(x-5)

All that's left is to multiply this out. (Just multiply two of these and then multiply that answer by the first factor.)
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