On a problem of Turán: (0, 2) quadrature formula with a high algebraic degree of precision

SummaryP. Turán has formulated a problem concerning a quadrature formula of the form(1) $$\int_{ - 1}^1 {f(x) dx \approx } \sum\limits_{t = 1}^n {(a,f(x_t ) + cf^n (x_i )),} $$ which has algebraic degree of precision at least 2n. We give a simple construction of such a quadrature, exact for all polynomials of degree 2n+1.