The parabola y=x2−15 intersects the x-axis at two points, P and Q. What is the distance from P to Q ?

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The parabola y = x 2 − 16 intersects the x-axis at two points P and Q. What is the distance from P to Q?

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Find the points P and Q.

These occur when y = 0, so 0 = x 2 − 6, and so x 2 = 6, which gives x = ± √ 12.

Points P and Q are then P = (− √ 12, 0) and Q = (√ 12, 0).

Distance between the two points is then q ( √ 12 − (− √ 12))2 + (0 − 0)2 = q (2√ 12)2 = √ 48 = 4√ 3

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