Question

If one root of the quadratic equation ax^+bx+c=0 is triple the other show that 3b^=16ac

Answer 1

ax²+bx+c=o
then, a=a. b=b. c=c
m+n = -b/a. and. m×n = c/a
if one root is triple of onother root
m=m. n=3×m

so,
m+n = -b/a
m+3m= -b/a
4m = -b/a
m= -b/4a

then,
m×n = c/a
m×3m=c/a
3m² = c/a
3(-b/4a)² = c/a. (m= -b/4a)
3(b²/16a²) = c/a
3b²/16a² = c/a
3b²/16a×a = c/a. (cross multiplication)
3b²/16a = c/1
3b² = 16ac