Manipal Entrance Test 2017 Math Paper

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