Question

If 3x²+6x+3 has roots a,b. then the equation having roots a²+3,b²+3 is

Answer 1

Given roots are a and b
i)sum of the roots =-b/a
a+b=-(6/3)=-2----(1)
ii) product of the roots =c/a
ab=3/3=1-----(2)
Do the square of (1)
(a+b)^2=4
a^2+b^2+2ab=4
a^2+b^2=4-2=2----(3)
If roots are a^2+3,b^2+3
i) sum of the roots =a^2+3+b^2+3
=a^2+b^2+6
=2+6=8
ii)product of the roots=(a^2+3)(b^2+3)
=a^2b^2+3a^2+3b^2+9
=1+3*2^2+9
=1+12+9
=22
Required equation
x^2-(sum of the roots)x+product of the roots=0
x^2-8x+22=0