If one root of the equation ax2 + bx + c = 0 is three times the other,

1.	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» 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 \(16\times\frac{c}{3a}=b^2/a^2\) \(16/3=b^2/ac\)

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»

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

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

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