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

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

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

\(16/3=b^2/ac\)