Since, a and b are the roots of equation x2−3x+1=0 ∴a+b=3 and ab=1 Now, the given roots are a−2 and b−2 ∴ Sum of roots =a−2+b−2=3−4=−1 and products of roots =(a−2)(b−2)=ab−2(a+b)+4=1−6+4=−1 ∴ Required equation is x2+x−1=0 Which is equivalent to x2+px+q=0 ∴p=1 and q=−1