Question

a quadratic polynomial has one of its zeros 1+√5 and it satisfies p(1)= 2.find the quadratic polynomial ​

Answer 1

Answer:

Given α = 1 + √5 So, β = 1 – √5 α + β = 2; αβ = 12 - (-√5)2 = 1 - 5 = -4 The quadratic polynomial is p(x) = x2 – (α + β)x + αβ p(x) = k(x2 – 2x – 4) p(1) = k(1 – 2 – 4) = -5k Given p (1) = 2 -5k = 2 k = -2/5 ∴ p(x) = (-2/5)(x2 - 2x - 4)Read more on Sarthaks.com - https://www.sarthaks.com/906928/quadratic-polynomial-has-one-its-zeros-5-and-it-satisfies-find-the-quadratic-polynomial