The curve y=2x²-3x-4 crosses the x-axis at P and Q.The tangents to the curve at P and Q meet at R. The normals to curve at P and Q meet at S. Find the distance RS.

Expert Answers

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First, find where the curve  crosses the x-axis by factoring: y = 2x² - 3x - 4 = (2x + 1)(x - 2). So the points P and Q are at (-1/2,0) and (2,0).

Next, we need to know the slope of the curve at the points P and Q to construct tangent lines there. y' = 4x - 3. So the slope at P is -5 and the slope at Q is 5.

Now we know the equations of the tangent lines because we have the slope and a point that they pass through, P and Q.

y - 0 = -5(x - -1/2) --> y = -5x - 5/2

y - 0 =  5(x - 2)     --> y = 5x - 10

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