How do you find all the zeros of #f(x)= 2x^3 + 3x^2+ 8x- 5#?

Answer 1

#f(x)# has zeros #1/2# and #-1+-2i#

#f(x) = 2x^3+3x^2+8x-5#
By the rational root theorem, any rational zeros of #f(x)# are expressible in the form #p/q# for integers #p, q# with #p# a divisor of the constant term #-5# and #q# a divisor of the coefficient #2# of the leading term.
That means that the only possible ratioanl zeros of #f(x)# are:
#+-1/2, +-1, +-5/2, +-5#

We find:

#f(1/2) = 2/8+3/4+8/2-5 = 1/4+3/4+4-5 = 0#
So #x=1/2# is a zero of #f(x)# and #(2x-1)# a factor:
#2x^3+3x^2+8x-5#
#= (2x-1)(x^2+2x+5)#
#= (2x-1)((x+1)^2+2^2)#
#= (2x-1)((x+1)^2-(2i)^2)#
#= (2x-1)(x+1-2i)(x+1+2i)#

Hence the other two zeros are:

#x = -1+-2i#
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Answer 2

To find all the zeros of the function ( f(x) = 2x^3 + 3x^2 + 8x - 5 ), you can use various methods such as factoring, synthetic division, or numerical methods like Newton's method. However, for cubic polynomials, it's not always possible to find exact solutions using simple methods. In this case, you might need to use numerical methods or software to approximate the zeros.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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