MathDB

Problem 4

Part of 1979 Bulgaria National Olympiad

Problems(1)

larger root of quadratic, parameter involved

Source: Bulgaria 1979 P4

6/17/2021
For each real number kk, denote by f(k)f(k) the larger of the two roots of the quadratic equation (k2+1)x2+10kxāˆ’6(9k2+1)=0.(k^2+1)x^2+10kx-6(9k^2+1)=0.Show that the function f(k)f(k) attains a minimum and maximum and evaluate these two values.
quadraticsparameterizationfunctionPolynomialsalgebra