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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 $a x^{2} + b x + c = 0$ 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 $a x^{2} + b x + c$ is an exact fourth power for all integers $x$ . Prove that $a = b = 0$ .