If (alpha) and (beta) are the roots of the equation (2x^{2} – 7x + 4 = 0), find the equation whose roots are (frac{alpha}{beta}) and (frac{beta}{alpha}).
Explanation
(2x^{2} – 7x + 4 = 0)
(alpha + beta = frac{7}{2})
(alpha beta = frac{4}{2} = 2)
(frac{alpha}{beta} + frac{beta}{alpha} = frac{alpha^{2} + beta^{2}}{alpha beta})
= (frac{(alpha + beta)^{2} – 2alpha beta}{alpha beta})
= (frac{(frac{7}{2})^{2} – 2(2)}{2})
= (frac{(frac{49}{4} – frac{16}{4})}{2})
= (frac{33}{8})
(frac{alpha}{beta} times frac{beta}{alpha} = 1)
(therefore Equation : x^{2} – frac{33}{8}x + 1 = 0)