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Problem #PRU-60855

Problems Algebra and arithmetic Polynomials Quadratic polynomials Quadratic equations. Formula for the roots. Quadratic equations. Vieta's rule. Calculus Real numbers Rational and irrational numbers

One of the roots of the equation $x^{2} + a x + b = 0$ is $1 + \sqrt{3}$ . Find $a$ and $b$ if you know that they are rational.

Problem #PRU-111345

Problems Calculus Integral Applications of integration Area by integration Algebra and arithmetic Polynomials Quadratic polynomials Quadratic equations. Vieta's rule.

The numbers $p$ and $q$ are such that the parabolas $y = - 2 x^{2}$ and $y = x^{2} + p x + q$ intersect at two points, bounding a certain figure.

Find the equation of the vertical line dividing the area of this figure in half.