# If one root of the equation ax^2 + bx + c = 0 is three times the other, then b^2 :ac = A. 3: 1  B. 3 : 16  C. 16 : 3  D. 16 : 1

21 views

closed

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

+1 vote
by (10.4k points)
selected by

In the given equation ax2 + bx + c = 0

Let α and β be the two roots

Given α = 3β ……..1

α β = (product of the roots)

3 β2 = c / a ……….. by using 1

β2 = …………….2

α + β = $-b/a$

4β = $-b/a$

Squaring both the sides

16 β2$b^2/a^2$

By using 2

$16\times\frac{c}{3a}=b^2/a^2$

$16/3=b^2/ac$