(a) Given that (frac{5y – x}{8y + 3x} = frac{1}{5}), find the value of (frac{x}{y}) to two decimal places.
(b) If 3 is a root of the quadratic equation (x^{2} + bx – 15 = 0), determine the value of b. Find the other root.
Explanation
(a) (frac{5y – x}{8y + 3x} = frac{1}{5})
(5(5y – x) = 8y + 3x implies 25y – 5x = 8y + 3x)
(25y – 8y = 3x + 5x implies 17y = 8x)
(therefore frac{x}{y} = frac{17}{8} = 2.125 approxeq 2.13)
(b) (x^{2} + bx – 15 = 0)
Since x = 3 is a root of the equation, f(3) = 0.
(3^{2} + 3b – 15 = 0 implies 3b = 6)
(b = 2)
(therefore) The equation is (x^{2} + 2x – 15 = 0)
(x^{2} – 3x + 5x – 15 = 0 implies x(x – 3) + 5(x – 3) = 0)
((x – 3)(x + 5) = 0)
The second root of the equation is x = -5.