Question

Stoc Lecture M/W... 4. (6 points) Recall that while the graph of y = z crosses the 2-axis in a distinct direction (let's call this an ordinary zero), the graph of y r is tangent to the z-axis at 1-0. We say that the latter function has a double sero. Since the derivative of y n sy 23, we see that taking the derivative at a double zero seems to produce an ordinary zero. x. 4 y . . More generally, we say that a polynomial p() has a double zero at := 0 if it can be factored as P(x) = 2h(x), where h(0) 0. (a) (2 points) Apply the product rule to p(x) = 2*)(a) to compute p(x). (b) (4 points) Factor your result from the previous part, and explain in one or two complete sentences why you know that p() has an ordinary zero.

Answer 1

- a Pla)= a 2 hlas Pilas = 0 a Cash (as] pile) = gele chea)] + dd (22) nya) za? nila) trao hlas plla)= asn'zal teahla) bi plla)= a Canica) +2 hlas] pllo) zoconllos tano)] PILO) = 0 pllol=0 pical has an oddinary zero.