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p(x) is a polynomial given by: p(x) = -2x + 8x2 - 1

At which of the following points will the graph of p(x) intersect the positive x-axis?

(i) 1/2

(ii) 1/4

(a) only (i)

(b) only (ii)

(c) both (i) and (ii)

(d) (none, it never intersects positive x -axis)

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Best answer

Correct option is (a) only (i)

Explanation:

-2x + 8x2 - 1 = 0

8x2 - 2x - 1 = 0

8x2 + 2x - 4x - 1 = 0

2x(4x + 1) -1(4x + 1) = 0

(2x - 1) (4x + 1) = 0

2x - 1 = 0 , 4x + 1 = 0

2x = 1, 4x = -1

x = 1/2, x = -1/4

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