Answer to Question #103702 in Algebra for Sourav mondal

Question

Use the Cauchy-Schwarz inequality to solve x³-25x²- 4x+ 100= 0 if we know that all its roots are rational.

Answer 1

$x^{3}-25x^{2}-4x+100=0$ then $x^{2}(x-25)-4(x-25)=0$ then $(x^{2}-4)(x-25)=0$ hence $x_1=2,x_2=-2,x_3=25$