If a and b are rational and b is not perfect square, then the quadratic equation with rational coefficients whose one root is 3 a+ b is

Step-by-step solution

We know that, in a quadratic equation with rational co-efficient, surd roots occur in conjugate pairs. So, other root will be 3 a- b . Quadratic equation will be x^2-( sum of roots ) x+ Product of roots =0 aligned x^2-(3 a- b +3 a- b ) x +(3 a+ b )(3 a- b )=0 aligned or, x^2-6 a x+9 a^2-b=0