The number of positive roots is the number of changes of signs there are, then decrease by 2 each time and stop when you get to 1 or 0
negative roots, sub every x with -x and reevaluate, count change of signs
decrease by 2 each time and stop when you get to 1 or 0
y=+2x⁵-x⁴-2x³+4x²+x-2
+,-,-,+,+,-
1 2 3
3 or 1 positive roots
replace x with -x ( baically flip all signs of odd powerd numbers)
y=-2x⁵-x⁴+2x³+4x²-x-2
-,-,+,+,-,-
1 2
2 or 0 negative roots
3 or 1 positive roots
2 or 0 negative roots
2nd option is answer
Answer:
(-2, -4.5)
Step-by-step explanation:
Answer:B
Step-by-step explanation:
If <em>x</em> = -1, you have
2(-1) + 3 cos(-1) + <em>e</em> ⁻¹ ≈ -0.0112136 < 0
and if <em>x</em> = 0, you have
2(0) + 3 cos(0) + <em>e</em> ⁰ = 4 > 0
The function <em>f(x)</em> = 2<em>x</em> + 3 cos(<em>x</em>) + <em>eˣ</em> is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < <em>c</em> < 0 such that <em>f(c)</em> = 0.
5.871 is greater than 5.781 because in the tenths place 8 is greater than 7. Also if you round the numbers to the nearest tenth, you get 5.9 versus 5.8