find out÷ 5 into 3 raise to the power x into -2x² into 6x³
Answers
Answer:
The root factor theorem tells us that if 3 is a root of 6x³–17x² ? 5x+6, then x-3 is a factor, and vice-versa.
The unknown operation is subtraction in this case. I assume its omission was an error.
((6•3–17)•3–5)•3+6 = ((1)•3–5)•3+6 = (-6) + 6 = 0
To find the other roots, we may reduce the degree by dividing the cubic by x-3.
6x³–17x² – 5x+6 = (x–3) • ( 6x²+x-2)
The quadratic formula gives the roots of the second factor as –2/3 and 1/2.
From the leading coefficient we know the cubic is negative when x is far negative, and positive for x-far-positive.
The derivative is 18x²–34x–5, with roots at about x = –1/7, and x = 2+ . Using 0 for the first in the cubic gives ymax about 6 . Using 2 gives ymin about 48 – 68 –10 + 6 = –24. Which, along with the roots should be good enough info to sketch: