For a given value of k, the product of the roots of x2−3kx+3k2−7=0  is 5. The roots may be characterized as

The given equation is x2−3kx+3k2−7=0 Product of the roots is 5⇒3k2−7=5 ⇒  k=  ±2. The equation becomes x2±6x+5=0 It can be write as x2±5x±x+5=0 ⇒x=±5, ±1 ∴  roots are either −1,−5  or 1,  5 , which are integral.