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Is 3,2 the correct answers to the bottom box, and how do you get the answer?

0 votes
1-1/x=6x^2
asked Nov 6, 2014 in ALGEBRA 2 by doan12345 Pupil

1 Answer

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The rational equation 1 - (1/x) = 6x2

(x - 1)/x = 6x2

x - 1 = 6x3

6x3 - x + 1 = 0

Now solve the above cubic equation.

Now find zeros of polynomial f(x) = 6x3 - x + 1.

Graph

The points where it crosses the x axis  will give solutions to the polynomial function .

The graph crosses the x - axis at a point that would suggest a factor.

It crosses the x - axis at one point hence there are one real root.

x  = -0.65034

Use synthetic division to determine if the given value of x is a root of the polynomial.

image

Since f(-0.6503) = 0, x = -0.6503 is a zero.

The depressed polynomial is  6x2 - 3.9018x + 1.5373

Since the depressed polynomial of this zero, 6x2 - 3.9018x + 1.5373 = 0, is quadratic,

Use the Quadratic Formula to find the roots of the related quadratic equation ax2 + bx + c = 0

a = 6, b = - 3.9018, c = 1.5373

Roots are

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Solutions are x = - 0.6503 and x = 0.3251 ± 0.388i.

answered Nov 6, 2014 by david Expert
edited Nov 6, 2014 by david

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