Question

if one root of the equation x^2 + bx + c = 0 is 4 times the other, then prove that 4b^2 = 25c

Answer 1

Let one root be m and another be n.
We know that m+n= -b ; mn =c and m=4n

So 4n+n = -b .....(1)
or n = -b/5
Again 4n²= c .....(2)
Putting the value of equation 1 in 2
4b²/25 = c
or 4b²= 25c