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Problem #PRU-116445

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

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

Problem #PRU-78043

Problems Methods Methods of calculus Monotonicity and boundedness Pigeonhole principle Pigeonhole principle (other) Algebra Polynomials Quadratic polynomials

The expression \(ax^2+bx+c\) is an exact fourth power for all integers \(x\). Prove that \(a=b=0\).