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Problems Methods Methods of calculus Continuity considerations Algebra and arithmetic Polynomials Quadratic polynomials Investigating the quadratic polynomial

13–15 2.0

Is it true that, if \(b>a+c>0\), then the quadratic equation \(ax^2 +bx+c=0\) has two roots?

Problem #PRU-86508

Problems Set theory and logic Mathematical logic Mathematical logic (other) Algebra and arithmetic Polynomials Quadratic polynomials Quadratic equations and systems of equations

13–14 2.0

Solving the problem: “What is the solution of the expression \(x^{2000} + x^{1999} + x^{1998} + 1000x^{1000} + 1000x^{999} + 1000x^{998} + 2000x^3 + 2000x^2 + 2000x + 3000\) (\(x\) is a real number) if \(x^2 + x + 1 = 0\)?”, Vasya got the answer of 3000. Is Vasya right?