If α and β are the roots of the equation 2 x 2 + 4 x - 5 = 0 , then the equation whose roots are 1 2 α - 3 and 1 2 β - 3 is

Step-by-step solution

Substituting y = 1 2 α - 3 , we get, 2 α = 1 y + 3 ⇒ α = 1 2 1 y + 3 Since, α is a root of the given equation ⇒ 2 1 2 1 y + 3 2 + 4 1 2 1 y + 3 - 5 = 0 ⇒ 2 1 + 3 y 4 y 2 2 + 4 1 + 3 y 2 y - 5 = 0 ⇒ 1 + 3 y 2 + 4 y 1 + 3 y - 5 × 2 y 2 = 0 ⇒ 1 + 9 y 2 + 6 y + 4 y + 12 y 2 - 10 y 2 = 0 ⇒ 11 y 2 + 10 y + 1 = 0 Hence, the required equation is 11 x 2 + 10 x + 1 = 0