Theory question 111
Quadratic Equations(a) The roots of the equation 2x2 + (p + 1)x + q = 0, are 1 and 3, where p and q are constants. Find the values of p and q.
(b) The weight of an object varies inversely as the square of its distance from the centre of the earth. A small satellite weighs 80kg on the earth's surface. Calculate, correct to the nearest whole number, the weight of the satellite when it is 800 km above the surface of the earth. [Take the radius of the earth as 6,400 km]
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(a) The equation is 2(x − 1)(x − 3) = 2x2 − 8x + 6 = 0.
Compare: p + 1 = −8, so p = −9; q = 6.
(b) W = k/d2. On the surface d = 6400 km; at 800 km up, d = 7200 km.
W = 80 × (6400/7200)2 = 80 × 64/81 ≈ 63.2, so about 63 kg.
Distance is measured from the centre of the earth, so add the radius to the height.