If one of the roots of the equation x2 + ax + 3 = 0 is 3 and one of th

1.	If one of the roots of the equation x2 + ax + 3 = 0 is 3 and one of the roots of the equation x2 + ax + b = 0 is three times the other root, then what is the value of b ?
Answer» Let 3 and α be the roots of the equation x² + ax + 3 = 0 Then, sum of roots = 3 + α = – a ..(i), Product of roots = 3α = 3 ...(ii) From (ii) α = 1. ∴ Substituting a = 1 in (i), we get a = – 4. ∴ The second equation x² + ax + b = 0 becomes x² – 4x + b = 0. Let β and 3β be the roots of this equation. Then, sum of roots = β + 3β = 4 ⇒ 4β = 4 ⇒ β = 1 and Product of roots = β × 3β = b ⇒ 3β²= b ⇒ b = 3.

If one of the roots of the equation x2 + ax + 3 = 0 is 3 and one of the roots of the equation x2 + ax + b = 0 is three times the other root, then what is the value of b ?

Answer»

Let 3 and α be the roots of the equation x² + ax + 3 = 0

Then, sum of roots = 3 + α = – a ..(i), Product of roots = 3α = 3 ...(ii)

From (ii) α = 1. ∴ Substituting a = 1 in (i), we get a = – 4.

∴ The second equation x² + ax + b = 0 becomes x² – 4x + b = 0.

Let β and 3β be the roots of this equation. Then, sum of roots = β + 3β = 4 ⇒ 4β = 4 ⇒ β = 1 and Product of roots = β × 3β = b ⇒ 3β²= b ⇒ b = 3.