Maths (Honours) questions(Algebra+differentiation)- Help! Urgent!

cocopopsxx

I really can't solve these two questions so need help asap.

q1) One root of ax^2 + bx + c =0 differs by 3 from the other root. Show that b^2 = 9a^2 + 4ac.

q2) F(x)= ax^3 + bx^2 + cx + d where a,b,c,d are constants. It has turning points at X=x1 and X=x2 and a point of inflexion at X=x3. Show that x1 + x2 = 2x3.

(The X=x1, X=x2, X=x3 thing is actually like the newton/raphson x1 but I don't know how to type it :P)

Any help would be appreciated! xxx

luciemc

Q1:
-use -b formula to find the two roots in terms of a,b,c
-subtract bigger root from smaller root and let equal 3
...simplify by doing a bit of squaring and this will give you your answer...

Q2:
-find first derivative and let equal 0 to find x1 and x2
-add them to give -2b/3a
-find second derivative and let equal zero to find x3
-x3=-b/3a
-this shows x1+x2=2x3

does this make sense...? i COULD write it out and scan but scanner is in another room and im lazy