Target Mathematics

1.42: Relationships between roots

4PM1/1/June/2018 — Question 2 · 7 marks

The equation 3x25x+4=03x^2-5x+4=0 has roots α\alpha and β\beta.
Without solving this equation, form a quadratic equation with integer coefficients that has roots
α+12βandβ+12α\alpha+\dfrac1{2\beta}\qquad\text{and}\qquad\beta+\dfrac1{2\alpha}
(7)