Question

If a and B Are the roots of the quadratic equation x +(p-3)x-2p =3 (p belongs to R), then the minimum value of (a^2+ B^2 + ab), is​

Answer 1

Step-by-step explanation:

a+b=-b/a

a+b=-(p-3)/1

squaring both the side

(a+b)^2=-(p-3)^2/1^2

a^2+b^2+2ab=-(p^2+9-6p)

ab=c/a

ab =-2

a^2+b^2-4=-p^2-9+6p

a^2+b^2=-p^2-9+6p+4

a^2 + b^2=-p^2-5+6p

a^2+b^2+ab=-p^2-5+6p-2

=p^2-7+6p