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A positive rational root of the equation...

A positive rational root of the equation `4x^3-x^216x-4=0` is

A

`1/4`

B

`1/2`

C

`3/4`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Plot the graph of `y=4x^3-x^2+16x-4` in the standard window and zoom in once to get a clearer picture of the location of the zero. Use CALC/zero to determine that the zero is at x=0.25.
An alternative solution is to use the Rational Roots. Theorem to determine that the only possible rational roots are`+-1,+-2,+-4,=-1/2,1/4`. Synthetic division with these values in turn will eventually yield the correct answer choice.
Another alternative solution is to observe that the left side of the equation can be factored: `4x^3-x^2+16x-4=x^2(4x-1)+4(4x-1)=(4x-1)(x^2+1)=0`. Since `x^2+1` can never equal zero, the only solution is `x=1/4`. [4]
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ENGLISH SAT-MODEL TEST 3-MCQ
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  2. What is the ranger of the function f(x)=x^2-14+=34 ?

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  3. A positive rational root of the equation 4x^3-x^216x-4=0 is

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  4. The norm of vector vecV=3veci-sqrt2vecj is

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  11. If 4 sinx+3=0 on 0lexlt2pi, Then x=

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  17. What is the domain of f(x)=3sqrt(15-x^2)?

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  18. Which of the following is horizontal asymptote to the function f(x)=(3...

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