Question

If one root of the equation ax^{​​​​​2}+bx+c=0 is three times the other, then b^{​​​​​​2} : ac =

Answer 1

let the roots be alpha and 3alpha

alpha+3alpha = -b/a

4alpha = -b/a

alpha = -b/4a ------(1)

alpha*3alpha = c/a

3(alpha)^2 = c/a -----(2)

substitute (1) in (2)

3(-b/4a)^2 = c/a

b^2/16a^2 = c/3a

b^2 = (16a^2*c)/3a

b^2 = 16ac/3




b^2 : ac = 16ac/3 : ac = 16ac : 3ac = 16 : 3