Question

If one root of the equation ax² + bx + c = 0 is three times the other, then b² :ac =
A. 3: 1
B. 3 : 16
C. 16 : 3
D. 16 : 1

Answer 1

Answer:

d. 16:1 I I think thank you mate

Answer 2

Let α and β be the roots of quadratic equation ax² + bx + c = 0 in such a way that α = 3β.

Here a=a, b=b, c=c

Then,

according to question sum of the roots

α + β = -b/a

3β + β = -b/a

4β =  -b/a

α = -b/4a .... (1)

And the product of the roots

α.β = c/a

3β * β = c/a

3β² = c/a

β² = c/3a ..........(2)

putting the value of β = -b/4a in equation (2)

-b/(4a)² = c/3a

b²/16a² = c/3a

b² = c/3a * 16a²

b² = 16ac/3

b²/ac = 16/3

b²:ac = 16:3