Let be an integer

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Let

k

be an integer. The possible ages (in years) of two siblings are modelled as the roots of the quadratic equation

x^{2}-(k+4)x+k+2=0

. (i) Obtain the condition on

k

for which the equation has distinct real roots. (ii) Using the sum and product of roots, find all integer values of

k

for which both roots are positive integers.