Question

If a and b are roots of the equation x^2 - 6*x+6 =0 find the value of 2(a^2+b^2)

Answer 1

we know that a and b are the roots of this equation

sum of roots(a+b)= -b/a=6

product of roots(a×b)=c/a=6

using the formula (a+b)^2= a^2+b^2+2ab

so, 6^2=a^2+b^2+2×6

36=a^2+b^2+12

36-12= a^2+ b^2

hence,,the value of 2(a^2+b^2) will be equal to 2×24=48