Question 3 - Turning points — a degree-n polynomial has at most n-1 turning points Practice

Question 3

00:00Est. 3 min

Marks:+3.000.00

Passage

Consider a polynomial

p(x)=(x^2-1)(x^3-4x^2+4x)(x^3-10x^2+33x-36)

such that

t(x)=(x^3-6x^2+9x)

divides

p(x)

s(x)=(x^2-5x+4)

divides

p(x)

q(x)

is the quotient when

p(x)

is divided by the polynomial

z(x)=(x+1)t(x)s(x)

. Use this information to answer the given subquestions:

Question

m

is the number of distinct roots and

n

is the number of turning points of the polynomial

p(x)

, then find the value of

m+n

Comprehension

Hard Difficulty

16 July 2023

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