1.13: Real roots and transformed roots

4PM1/2R/November/2020 — Question 7 · 12 marks

(a) Find the set of values of k\displaystyle k for which the equation
kx2−4x+2k=7kx^2-4x+2k=7
has real roots.
(4)
Given that the roots of the equation are α\displaystyle \alpha and β\displaystyle \beta,
(b) form a quadratic equation with roots
α+1αandβ+1β.\frac{\alpha+1}{\alpha} \qquad \text{and} \qquad \frac{\beta+1}{\beta}.
Give each coefficient in terms of k\displaystyle k.
(8)