We have zeros at: -5, 1/2, 4 and -3 Which of the following functions is the poly

Question

We have zeros at: -5, 1/2, 4 and -3 Which of the following functions is the polynomial of thelowest degree w/ the values above? I'm going to skip the f(x) = w/ a thru d below. a. x(x+5)(x -1/2)(x-4)(x+3) b.   (x-5)(2x+1)(x+4)(x-3) c. (x+5)(2x-1)(x-4)(x-4)(x+3) d.   2x(x+5)(x-1/2)(x-4)(x+3) Please show details.   We have zeros at: -5, 1/2, 4 and -3 Which of the following functions is the polynomial of thelowest degree w/ the values above? I'm going to skip the f(x) = w/ a thru d below. a. x(x+5)(x -1/2)(x-4)(x+3) b.   (x-5)(2x+1)(x+4)(x-3) c. (x+5)(2x-1)(x-4)(x-4)(x+3) d.   2x(x+5)(x-1/2)(x-4)(x+3) Please show details.  

Explanation / Answer

The answer is c. f(x) = (x+5)(2x-1)(x-4)(x-4)(x+3) An easy way to check this solution is to plug in each of thenumbers given and the resulting equation should equal 0. Thus if x= -5, the term (x+5) = (-5+5) = 0. The same is true if you plug in1/2, 4, and -3, at least one term must equal 0. The problem thenwith a & d is that these polynomial also have a zero at x = 0,which given the initial conditions cannot be correct.

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