Which of the following sets contains all roots of the polynomial f(x)=2x^3+3x^2-3x-2?
1 answer:
Answer:
C
Step-by-step explanation:
Given
f(x) = 2x³ + 3x² - 3x - 2
Note that
f(1) = 2 + 3 - 3 - 2 = 0 , thus
(x - 1) is a factor
Dividing f(x) by (x - 1) gives
f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)
To find the roots equate f(x) to zero, that is
(x - 1)(x + 2)(2x + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x + 2 = 0 ⇒ x = - 2
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
The solution set is therefore
{ - 2, - , 1 } → C
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a) A square is a rectangle. True
Reason: Property of Rectangle: (i) Opposite sides are equal and parallel. (ii) Each angle is 90 (iii) Diagonals are equal and bisect each other.
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b) A polygon with 21 sides has 432 possible diagonals. False
Reason: Number of diagonals of a polygon =
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c) All three angles in an Isosceles triangle are equal. False
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d) The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°. True.
Reason: The sum of measures of the exterior angles of any polygon is 360