Calculate. y=3x^5 +5x^4 -2x^3

Noelanijd 2022-07-27 Answered
Calculate. y = 3 x 5 + 5 x 4 2 x 3
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Answers (2)

Brenton Gay
Answered 2022-07-28 Author has 13 answers
X intercepts coorespond to the x coordinates where y = 0. Setting the function equal to 0
3 x 5 + 5 x 4 2 x 3 = 0
Factoring out x cubed
x 3 ( 3 x 2 + 5 x 2 ) = 0
Factoring our quadratic
x 3 ( 3 x 1 ) ( x + 2 ) = 0
the whole thing will be zero if any of the above factors are zero
x 3 = 0
x=0
3x-1=0
3x=1
x = 1 3
x+2=0
x=-2
So the x intercepts are -2, 0, 1/3

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Bruno Thompson
Answered 2022-07-29 Author has 9 answers
Substitute z = x 4 . Then, the equation reads y = 3 z 2 + 5 z 2.
Using the Pythagorean theorem ( z = [ b ± b 2 4 a c ] / 2 a, where a = 3, b = 5, and c = -2: z = [ 5 ± 52 ( 4 3 2 ) ] / ( 2 3 ) = [ 5 ± 25 + 24 ] / 6 = [ 5 ± 49 ] / 6 = [ 5 ± 7 ] / 6 produces two solutions: 2/6 = 1/3 OR -12/6 = -2.
Therefore, the two z-intercepts of the substituted equation are z =1/3 and z = -2.
However, since we substituted z = x 4 earlier, now to find our x-intercepts, we have x = ( 1 / 3 ) 4   a n d   x = ( 2 ) 4 . Thus, our solutions are x= 1/81 and x = 16.

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